The 3rd Round distribution on March, do I need to sent my previous byteball balance to new wallet, like 2nd round distribution?
And do I need to linked my new BTC address? or I can use my previous BTC address? which is I use for 2nd round.
You have answers in your questions. YES & YES

I am confused. I guess both answers should be "NO" if I have not moved my funds after the 2nd distribution?
If my understanding is incorrect, please anyone can explain in a bit more details why?
try to communicate with the bot in the BB wallet, just check if your BTC address is linked.