yes, you can open two accounts. And yes there might be service charge if your monthly balance is below some amounts depend on the account type you have.
To Chase, for a saving account, you should at least put 300.00 USD in it. For Checking account, you should at least use it to pay bills for 5 times per month. Otherwise, each of them will be charged some amount of service fee.
To Citi, they do not inform me that I have to put some money in both accounts for a waive of service fee. But I will check whether it is true.