Help needed..

What terminal said. I sometimes get the board out, lay it on the board bag and rig a sail to go on it. With this set-up you can practice your basic moves, and more advanced if you want, get used to the weight of the sail and where you put your feet etc. Should help pass the time over a long Winter and get you tuned and fired up for Summer.
Carve gybing needs speed and commitment and plenty of practice, if you perservere long enough you will get it. I've watched it hundreds of times on videos, it is surprising what you pick up from them and I still notice things that I can improve. I'd try practicing the move and then comparing it to what happens on the screen. Most important tip I can give you is to try to keep your weight forward so as not to sink the tail.
You don't use your sail for steering in the carve, it is all foot steering. As you are travelling off the wind there is no weight in the sail to use for steering anyway.
Next core skill? Whatever you like to practice. If you can't water start that is probably a biggie.

I used a simulator like this at the place where I first hired a windsurfer.

This one is rotating a bit too freely, it should have a bit of drag to simulate the board turning in the water, but it is a stage up from just bolting the mast base onto a large plank.

You don't need a windsurf board, just a large sheet of plywood if you wanted to build one, but you can do a lot of sail training with the mast just bolted onto a static wood plank.

Terve,Answers to your questions:1. All boards and sails do carve, but you had to plane before that. 2. No3. Learn to plane footstraps and harness lines attached. Also water start is good to learn. After that it's time to focus carve jibes.4. Freeskate or skimbat! Some of us also travel in wintertime for windsurfing. You can also spent some time in www.purjealutaliitto.fi ;)