How ban system works in BF4

That depends on the type of ban. If you were banned only by a single server then that means that you can't play on that server but you can play on all other servers. If you have a Battlelog ban that means that you can still play Battlefield but just can't interact with others on Battlelog. If you have an EA ban you cannot access your Origin account. If you have a Punkbuster or Fairfight ban that means that you cannot play on servers that use punkbuster or fairfight anti-cheat software but you can play on other servers that do not use those programs.

Regarding the second part of your question, we do not assist players in finding ways to circumvent bans. If the Ban was given by EA any alternate accounts will also be banned upon discovery.