Re: 1 There are some good threads on modifying one of the relay contacts to enable the top to operate with the engine running, but I'll be damned if I can find it. The fix is simple. You need to put tape on the correct terminal of the relay to insulate it and prevent an electrical connection. I was going to post the URL for you, but you'll have to do your own search. I first searched this site, and can't find anything. If it is found, it should probably be moved to the topic area call "Posts that every 968 owner should read". Send a PM to Eric when you find it.
I searched on "convertible", "cab top" and one or two other variations, but couldn't find the posts. I think there is at least one topic, maybe two, with quite a few messages and some real valuable info.
I also searched the 968.net site, but could not find it. IIRC, the thread was started sometime in early 2005, so it wasn't that long ago.
Re: 2 - Don't think you need to; I never have.