Can I access my fiverr account( same a/c ) from different personal computer.
yes, you can. but do make sure, no one else uses that computer with same niche on Fiverr.
That means I would not login with other account from same computer?
Every person is allowed to run only 1 account on Fiverr. multiple accounts are against Fiverr TOS.
Can my friend access his fiverr account from my laptop?
Yes if he works in different category than yours as far as I know.