Have the convertible top half open and check between the gaps for obvious signs of damage such as frayed wiring, loose connections, physical defects, the roof is not bent and also check the roof locates AND locks into its dowels.
Sadly this is all that can be done at this point.
The i drive freezing is due to software error, when was the last software update done?
The problem turned out to be conflicting software integrated in the vehicle, the car is trying to communicate with control units that aren't there, hence the long start up time and freezing. This issue has been sorted out for every model but E60, but since the E63 are very similar, i might wait for the newest update of ISTA/P (Software updating program) which should be available in a couple of weeks.
Your convertible issue as mentioned above should be checked with BMW service and might require a switch or wiring repair. Your software update again can only be done by your nearest BMW dealer.