I've raced in a cut up sleeveless suit. It was fine - really looking forward a dedicated SwimRun suit this fall.
Trail running shoes work fine but companies like Inov-8 and Salming seem to be very popular.
Yes, paddles...prepare for them and get an appropriate size and it's fine - I have a bad shoulder so I use smaller paddles.
Yes - variety of ways to do it...not rocket science.

Most races are in cooler weather. Dedicated suits have front if not front and rear zippers. Not an issue for most races.
100% depends how hard you go. Swimming is a welcomed relief after running up or down a mountain in my experience.