1. If I moved around my BTC I will have to link those addresses to be part of the second distribution round;
Yes, or send your BTC back to your already linked addresses.
2. The same goes for the GBYTE: if I moved coins around I will have to do the same.
You will have to do the same (link) to get blackbytes associated with the bytes you'll get. Otherwise, no, because bytes will be sent to any address that holds bytes. So, if you want the blackbytes, keep your bytes on linked BB addresses.
3. I'm not sure about blackbytes but it should be the same, please correct me just in case.
Blackbytes do not matter in the distribution.
Last but not least, is there any possible date for the 2nd round?
Not yet.
Do we still go for mid-feb?
Yes.