Is there any rules against alpha open multi game?
Example: If I have 2 computer on 2 different network play on 2 alpha account. Will I get band?
Back then, account will be band if it shared with different user. Is that still the case?
Example: I have a old account want give to a friend so he can try EVE for the first time, will the account get band?
If I also login from time to time, will it get band?
3.Besides RMT, what other case account can get band? Where can I find those info that is up to date?
Yes, the EULA states that while playing on an Alpha account you can only be on that 1 account. the EULA applies to you as a person, not your PC(s).
I can’t really say for sure but I would guess that you won’t be banned because of it, however I would still very much advice against it as it may have unforeseen consequences. I’m unsure if you’d even be able to connect to server when your friend is playing.
So besides RMT, you will also be banned for using Programs or Contraptions that automates parts or all of EVE gameplay, this include Input-broadcasting (press 1 button and it sends input to multiple clients), commonly use in programs like ISBoxer, however using ISBoxer itself is not a ban-able offense only the input-broadcasting part of it is.