Lets also say that most "tweaks" will be to the common easy to change components - nose moment; tail moment; tail volume; wing tip shape, flap% of wing area; flap length (full or partial) and control ratio's. There are other areas that the original designer might change - airfoil thickness and area, as well as shape but for now lets do the simple to get to ones.
As I said before, these "numbers" aren't of much value. You can measure them, but they don't mean much. The width of a car door, for example, might be some indication of wheelbase, but not necessarily. Nevertheless, I'll try to give you qualitative answers both in aero talk and in what phenomena to expect. Qualitative answers is all you'll get from anybody except Serge, because we either are too lazy to give quantitative answers or we don't know how.
"Nose moment" is unknown in the aeronautical literature, but I'll guess that stunt fliers define it as the distance from the propeller to somewhere else on the airplane. I may have found its origin: a simplification of moment of inertia that Wild Bill made in an article on stunt design. This has a bunch of effects, each of which should be covered separately. You ain't changing just one variable.
1. The farther forward the engine (or any other mass) moves in the airplane, the farther forward the CG will be if nothing is done aft of the CG to balance it. Moving the CG forward increases static stability in pitch and yaw. Moving the CG forward requires moving the leadouts forward to keep the same yaw angle relative to a tangent on the circle. Moving the CG forward will reduce the effects of bad stuff in your airplane: control friction, control slop, other causes of hunting. Moving the CG forward could make it easier to fly level on a calm day, but on a windy day the airplane will climb going upwind and dive going downwind. Moving the CG forward will require more elevator deflection for a given turn radius-- maybe more than is available. Moving the CG forward will increase control surface hinge moment for a given turn radius. Increased hinge moment makes the airplane harder to fly accurately if there is turbulence or if the airplane is mistrimmed: differences in line tension result in more varied control surface deflection.
2. The farther forward the engine (or any other mass) moves away from the CG (including moving the engine forward and adding weight to the tail to balance it), the higher the moment of inertia is about the affected axes. Moving the engine forward affects the pitch and yaw axes. In pitch, the higher the moment of inertia, the lower the static stability. Pitch damping will be reduced. The higher the moment of inertia, the more elevator it takes to get the airplane rotating and the more it takes in the opposite direction to stop the rotation. The higher the moment of inertia, the harder it is to avoid pitch and yaw oscillations.
3. Moving the propeller forward does not increase the gyroscopic effect of the rotating crankshaft and propeller.
4. Moving the propeller forward increases the effects of the propeller being at an angle to the airflow.
5. Moving the propeller forward gives a tad of effective engine offset.
6. Moving the engine mass forward changes the resonant frequency of the nose, and can exacerbate or quell vibration modes. Ax me about B-17 stunter engine resonances, a subject my ignorance of which was exposed multiple times.
"Tail moment" is unknown in the aeronautical literature, but I'll guess that stunt fliers define it as the distance between flap and elevator hinge lines, maybe at the airplane center if one is swept. It's sort of a race among the aerodynamic, elasticity, and mass effects of the tail length. I actually wrote stuff on this here on this very forum, but nobody read it. This isn't surprising, because hardly anybody read aerodynamic stuff I got paid a lot of money to write. Here is a combination of a couple of posts:
1. The effect of downwash: the more lift, the more downwash. Downwash is destabilizing: you put in a little up elevator, and the downwash acts as even more up elevator. Longer tails make this better.
2. Pitching moment due to pitch rate. This is caused by the change of angle of attack on the tail because of the air being round in a loop, rather than flat in level flight and maybe from the change in direction of the wind on the tail from airplane rotation. The longer the tail, the more negative pitching moment due to pitch rate is, hence the more stable the airplane is. Longer tails make this better.
3. Pitching moment due to rate of change of angle of attack. The tail contribution to this is maybe (according to Etkin) due to the time between when the wing starts making downwash and the downwash gets to the tail. I would reckon that this effect would make the airplane worse as tail length increases, but I don't know.
4. Contribution of pressure distribution on the tail to pressure distribution on the wing. An elevator hinged at the trailing edge of the wing acts as a flap going the wrong way, limiting the lift capability of the wing. Longer tails make this better, but may not have to be very long to make this evil go away. Maybe that's why the later, balanced-elevator Fierce Arrows fly better than the original.
5. Tail lift fighting wing lift. The longer the tail, the less it has to push down to rotate the airplane to the requisite angle of attack, hence the higher net airplane lift capability. Also, given the stabilizing effects of a longer tail, a longer tail lets you get away with a farther aft CG, hence even less force required of the tail. Longer tails make this better.
6. Structure and pushrod weight. Weight goes up fast as tails get longer, particularly if the airplane is designed to withstand indignities such as hitting the ground. Pushrods get fatter to maintain stiffness. Longer tails make this worse.
7. Pitch moment of inertial (barbell effect). Longer tails make this worse, although the leverage of longer tails helps them get the airplane rotating.
8. Ground handling (fitting into cars and shipping boxes). Longer tails make this worse.
9. Reduction in dynamic pressure at the tail due to wing "wake". Serge read something that Martin Simons wrote saying this is a big deal. It's not. Here is something quantitative:
http://naca.central.cranfield.ac.uk/reports/1939/naca-report-648.pdf 10. Sensitivity to CG position. The stabilizing effect of a longer (and larger) tail let you get away with a wider CG range. Longer tails make this better.
I had some of this stuff in mind when I came up with the Nemesis II combat plane as a kid. It had a way-longer tail than its contemporaries. I think the main things I had in mind were items 1., 4., 5., and 10. above. I found 1. in a library. I knew about 4. and 10. from a flying wing I made, which sucked.
I persisted in having longer-tailed combat planes than most. A Dane was teasing me about my Snort having a long, vulnerable tail at the 1990 world champs. He said he would cut it off. I thought that would be difficult for him to do with the Snort behind his plane nibbling his streamer.
"Tail volume" is an actual aeronautical term, but doesn't include some easy-to-include stuff that contributes to its aerodynamic effect-- wing and tail lift curve slopes that are functions of wing and tail aspect ratio, sweep, and taper-- nor some hard-to-include stuff such as 1. 4. and 9. in "tail moment" above. Its effects are about the same as for 5., 7., and 10. in "tail moment" above, but it also gives credit for tail area.
Wing tip shape doesn't do much. Flite Streak tips might work a little better in lift and drag, but I'll bet you can't feel the difference. They will adversely affect rolling moment due to sideslip, the effect of which is to narrow the region of the circle in which your maneuvers will come out right in the wind.
The more flap span / wing span you have,
1. The tighter the plane will turn, or the more margin you have at a given turn radius, assuming that there's enough elevator.
2. The less hinge moment you'll get for a given turn radius. See the deliterious effect of hinge moment in "nose moment" above.
3. The more prone the wing tips will be to stalling.
4. The potential for perversions from discontinuity at the end of the flap changes. It's most at maybe 80% span, but I don't know.
5. The more poop you'll need from the elevator.
6. Wing tip vortices and their effects for a given turn radius will not change.
7. The heavier your flap and wing structure will need to be (a simplification: ask PW to amplify it).
Flap chord / wing chord is tougher (I separated your area thing into span and chord). The more flap chord / wing chord you have,
1. The tighter the plane will turn, or the more margin you have at a given turn radius, assuming that there's enough elevator. There is an upper limit to how much of this benefit you'll get before it's swamped by the negative stuff.
2. The more hinge moment you'll get for a given turn radius. See the deliterious effect of hinge moment in "nose moment" above.
3. The potential for perversions from discontinuity at the end of the flap increases.
4. The more poop you'll need from the elevator.
5. Wing tip vortices and their effects for a given turn radius will not change.
6. The heavier your flap and wing structure will need to be (a simplification: ask PW to amplify it).
Control ratios of interest might be the flap / elevator ratio and the line displacement / control surface deflection ratio. You can calculate both (and linearize them for your airplane, if that's what you want) from my Excel-VBA program. Line tension difference due to hinge moment decreases with line displacement / control surface deflection ratio. Rich Porter and Paul Walker have thought about this, to some benefit for at least one of them. Increasing flap / elevator ratio:
1. Causes the airplane to rotate about a point farther back.
2. Will give less pitching moment for a given elevator deflection. This will reduce maneuvering capability and eventually cause you to run out of elevator authority, limiting maneuvering capability
3. Is what you need to do when the CG moves aft.
Flap / elevator ratio need not be constant. See Igor's mechanism and the Beringers' elastic flaps, noting that both have been on the World Champs podium.