is the car with i-drive or not?
The TPS system can be reset / initialised from in the cabin yes.
You can of course run regular tires on the e90 (almost everyone here does..)
Check if the !wheels! can have non runflats fittet though.. some have said there is a differance with the inner seal lip, and it gives problems when fitting non RF´s
The wheelspeed sensor, which is also in part the ABS sensor on the rear left i think cant be reset via the OBC. so its a dealer or someone with a GT1 tester.
As for non rf´s voiding your warranty... yeah, i think it does.. its an non OE part, so BMW wont cover it.
Sounds like something happened when mounting your wheel mabey? if they were a little over zealous when fitting, they could have tugged on the ABS sensor wire causing a prob..
Have a look at the connection for the 2 rear ABS sensors, There could be something there
Been there, done that, wanna do it again