If you have a normal coopers or homebrew shop fermentor - its not going to melt when you put the hot wort into it. If yo have a better bottle or something thats not made out of HDPE plastic, then I'm not so sure.
quite a few people no-chill in their fermentor - I personally don't think that its the best way to do it and suggest you get yourself a proper NC cube, but that doesn't mean it wonk work out just fine in your fermentor, it will.
Whether you bother with a secondary fermentor or not is up to you, it isn't strictly necessary, but it isn't going to hurt either - and after that you can bottle. If you are going to do any finings etc, you would do that in the secondary.
TB
edit - just remember that that fermentor is going to be a bit "squishy" from all the heat. I would be careful if you are planning on moving it while its still hot. And the tap will get knocked out a lot easier than it normally would so be careful.