Anyway, if the answers to the above questions were YES
The logical next step after the F4 would be the aerodynamic airframe of the K4, even with DB605A. Could be available middle /late 43 . Would be 25-30 km/h faster than G6 on same engine.
I agree. Even better, introduce those fixes like wheel well cover on the first 109G, as was originally intended (did anyone notice the straight sides wheel wells vs the rounded ones on the 109F?) And why those bulky HMG bulges were used when it must have been quite obvious to anyone that a elongated, streamlined cowling (as on the 109K proto) could be much better is beyond me.
A new ,under fuselage radiator could give some additional speed . The freed space at wings perhaps could accept small fuel tanks
Possibly doable, but would need a major redesign of the aircraft, since the fuel tank was already where a Mustang-style ducting would be. The Italian design had such, but the Germans criticized those for a) being too small capacity b) making it impossible to mount heavier bombs under the fuselage hardpoint. Note the size of italian wing bombs.. and droptanks.
Or introduce some type of combat flaps.
Already present, just manual.
Standart main wheels , not the enlarged of the K4. Long tail wheel. Accept the fact that it was a small air superiority fighter. Not use it as multi purpose fighter, with heavy equipment. Its structure and landing gear should be only strong enough to support the standart configuration (with the 605 engine) and a 300lt drop tank. No 30mm cannons,no rockets ,no bombs , no presurized cocpits, no fancy radios . All these required additional structural strength (=additional weight)
But tactically all these were very very useful. Also the larger main wheels were needed to cope with increased weight and added stability. BTW the larger main wheels were not a problem, but they were mounted in more right angles, which more or less fixed the looping tendency.
Improve its armament by introducing better guns I have read about the proposals and studies of a faster firing and lighter 20mm gun, and more powerful but little heavier 13mm HMG
IMHO the guns were all fine. The 13mm weak HMGs were light, fast firing and could penetrate any aircraft armor. That was all asked for.
Introduce flettner tabs IF the wing can handle the forces
Agree. It was a mistake that these were only introduced on certain batches.
Study the possibility for a sliding canopy similar to that of Ania S199. It seems to offer even better visibility than Erla canopy
Study the possibility to replace the under nose oil cooler with a cooler similar to that of D9
Study the usefulnes of a different attachement of the wing for higher speeds
Probably studied though and though not worth it.. I doubt the sliding canopy would have been any better, but one interesting (and unexplainable) thing was that the 109K proto featured a bulged-top canopy. The 109 canopy was fine, except for tall people. A small bulge would have easily fixed that, and ti was only one plexi panel to be changed. Perhaps they worried about canopy distortions.
Ensure good building quality
Use slipper fuel tanks to boost range
That would probably add a few km range and kph speed with a droptank - and would also mean that 109s would need a special droptank and could not use the standard droptank used by all other aircraft from fw190 through ju 87 to destoyers. A simply aerodynamic fairing between the tank and the fuselage was tried and was very effective in reducing drag, but probably not worth it. Increasing speed for cruise by 20 km/h in a four hour cruise adds what, 80 km to range?
Introduce as soon as possinle MW50 ,wide propellers and 603 supercharger
The problem is that the engine bearings/lubrication can't even handle 1500 HP until the autumn of 1943, much less 1800-1900.. though a 603 supercharger could be probably still used.
Simply replace it with an easier to produce version of the Fiat G55
They would end up with much fewer fighters with different set of problems.. the G55 was a good fighter, but costly and far from perfect IMHO. The Germans considered it seriously, even tested it, but declined in the end.