On the subject of the heavy tank (i think we were calling it the K-1?):
Test out the suspensions, drive train and engines. make sure they run well. Ideally try to make sure ware is either reduced to a minimum or eliminated in all meaningful ways. Then start work on the turret. ideally I'd personally want the turret to be a 3 man turret with ample extra room, to cater for more ammo when using a 40mm gun and more room for a larger gun when needed.
I mocked up what i would like the turret to look like. It is currently 'fitted' with a 110mm cannon:
On the hatch at the top which hasn't got slanted protection (the commanders hatch) there should be an MG attached for the commander to use when out the hatch.
Also, i think we should really think about converting the engines to diesel, as well as tuning them up so they are more powerful.
As for an APC: I support a modified version of the Badger. However, keep the Armour the same as the MK1 Medium tank and the 40mm turret and cannon, but up the engines to the two used in the MK2. Add in the firing slots and enough room to fit 8 men and we're done.
A Self Propelled artillery version of the MK2 badger should be built too, furthering what Brood said earlier but not on a halftrack base. Not sure what gun we should use, although if we do build it the gun would be the current 80mm cannon.
Moving on to planes, i support the previous notion that we should at least start looking into monoplanes and maybe looking into early jet engines (the first jet engines were designed by a British fighter pilot in 1926 parallel to the efforts of a German scientist in the same year).
Finally, i support the continued work on the Alexi, as well as any variants we come up with.