Top question

[Retroman1969]

My daily driver does this as well. Don't quote me because I'm not sure, but I believe there are elastic tension straps that are supposed to hold the fabric in place so it will slide into the channel as the top is being raised. If they're worn or gone, it does that. I don't know if they can be replaced separately of the top, haven't looked into it yet. Perhaps someone here can give a more educated answer.
Since mine does it on the drivers side, I actually stick my hand out and guide the edge into the channel while the top is going up. (don't try this at home kids! You could potentially get a nasty pinch!).

[Run]

As mentioned there are elastic straps. There is also a Velcro strap there that wraps around the frame as well as a guide string for lack of a better name that fits into a snap of sorts.

[Viper10000]

My top did the same thing after I replaced it. When operating the top I would make sure before its all the way closed that it would sit in the channel. After 2 or 3 times doing that I never had a problem. If you can get it to sit in the channel and then close the top, let it sit like that for a while and it should be good to go. ( at least that was my situation)