Stretching

Can I stretch sitting down instead of standing? And do I always have to wrap?

It’s your choice, if you feel more comfortable stretching while sitting, then do it, it’s not going to interfere on your gains anyway.

And some people say that hot wrap is the essential part of your PE’s routine, it makes your tunica more flexible, for example;

Standing or sitting doesn’t make a difference, so whatever is more comfortable for you is fine. I always warm up first, and I would advise you to do the same. Whether or not it has a positive effect on your routine might be debatable, but it definitely does not have a negative effect so warm up (and down)!