Since when you have a bank account you are technically loaning money to the bank and charging the bank interest, is this a violation of the negative mitzvah not to charge interest on a loan? Or for a Jewish owned bank only? Or not at all? I can't find an answer by Googling so far I am only seeing other bank related questions. I am talking about just having a normal bank account like a checking and/or savings account like every person has. Thank you!
If the bank is owned by a jew, they are not permitted to pay interest and you are not allowed to take it. See this source for the general principle of interest.
That being said, there is a halachiky correct way to pay interest on a loan to a jewish owned bank (or whowever loans the money). And presumably the jewish owned bank could have a similar way worked out to be able to pay the account holder interest according to halacha if they wanted to. See heter iska for more information.
Lastly, once in a while, there is an issue of getting interest on a bank account even if it was setup properly according to halacha. See this article when this occurs and how to properly deal with it. The article doesn't explain everything but it gives a source where one can further research the matter.