For the CP4 I'd say either reduce the POP cost (maybe 10?) or - my favourite - add utility.
Like an actual commander that increases sight range (not sure if it can be done model wise), some focus fire ability vs infantry or mark vehicle vs tanks (will probably need to be removed form the Elefant commander then), recon or smoke shell or something similar. Even some "inspire" ability or so would fit nicely.
Only one of these obviously, not the whole set
Agreed. I think the issues with the CP4 in 1v1 particularly is that the RD bonus is a relatively negligible effect on infantry unless we are talking specific situations like a full hp squad getting nailed with a single katyusha rocket.
Rushing it means you are using it as a shock anti infantry tank which means it competes directly against the ostwind and the standard P4 the latter being on par in shock value and the former being superior(against ai).
Late game fuel and mp cost is less of an issue as trying to find pop efficiency. The CP4 is not pop efficient enough for its aura to make up for its lack of combat ability. The ostwind will be an AA platform and provide good mobile AI and a P4 is going to be better at supporting a push as you can use it to flank enemy tanks.
And the mediocre range of the aura limits its usefulness because you have a moderately tanky medium tank that is required to stay extremely close to the frontline. What compounds this is if you are supporting an infantry on infantry battle, the CP4 will have limited usefulness as the enemy infantry won't hold their ground for long anyway due to the proximity of an anti infantry tank. But if you are supporting a force fighting against tanks, it won't be able to contribute anything except the aura.
Best case scenario is if you are fighting a mixed force which will stand its ground but also provide targets the CP4 can actually shoot at while simultaneously buffing enough of your units to make it worth having around. If that sounds really conditional, that's because it is.
My suggestion is remove the aura and make it an activated ability that buffs units around it for a limited duration like the luftwaffe supply crates. This way it doesn't need to be in the area for it to be benefitting the units who are defending or attacking. You can pop it prior to an advance or pop it and zoom away to stop a cap with it while your buffed units hold the line.
Recon would be nice as well, id say a loiter around the location it was called in. Cp4 could be required to be stationary or not. I dont think it should be a recon run that will let you call in a bomb strike on the other side of the map.