Yes, though getting opening first account is probably easier with a larger bank. Nobody is limited to having one account only.
Rates are subjective, I don't have any debts other than mortgage. Most credit cards are paid to 0 every month. Those not paid fully have promotional 0% APR for 12-15-18-24 months and will be paid fully before interest charges kick in. As to savings rates, I haven't seen many that offer better than HYSA accounts from big players.
Big online banks have 0 monthly fees without any requirements. Sure, service is a different thing. I personally have several of these accounts, never had issues. But my use case is limited: I don't deposit checks or cash, I don't withdraw money from ATM that often. If those used a lot, a more tranditional credit union / bank is preferred for sure.
Anyways, don't want to deviate from original question.
Based on this page, non residents can open bank accounts in Michigan - https://www.stateregstoday.com/living/opening-a-personal-checking-account-in-michigan