E70- need help..

[PastorDaddy]

Hi guys- need help and direction. My wife drove her 09 X5 through a very deep puddle during a torrential downpour in a poorly lit area- no visibility. Upon doing so, the motor died. Without fully knowing the dangers, she tried to restart the engine, to no avail. Eventually it did start, and was able to drive to safety -coughing and sputtering the whole way. The longer the vehicle sat, it seemed to slowly clear itself of the coughing and became more normal.
When I got to the scene, and saw that it was running, I assumed that if water had been ingested into the intake, the engine would've likely been locked, or would've been "blown".. But it clearly was running, no warning lights, and no appearant engine damage.
Now a day later, we started it, let it run for a while, and the coughing and sputtering has dissipated, and was showing signs of normal operation. Again with no warning lights.
Here's my question- what do I need to look at at this point to be certain all is well with her Beamer? Also- an engineer friend of mine suggested that I need to change all fluids in the vehicle- oil, trans, diff, and radiator. My thoughts- if it shows signs of no damage and normal running, then that would be less likely/impossible for any of the fluids to be compromised by rain water, or that any rainwater would've seeped in. Am I correct in this? Should I change any of the fluids? And as for the fluids, how can I check the integrity of the fluids with no dipsticks?
Any help or direction you guys have will be greatly appreciated!!
Thank you!