1.) I'm not sure what you mean by "3 checks/statements for this card", so I won't answer this question.
2.) You generally don't want a high balance. What is important is what balance is REPORTED. Lets say your statement ends on the 15th, but your bank reports you balance on the 30th. You would ideally want it paid off before the 30th, so it reports a zero balance, or at least gets it down to a small balance. If it is always reporting at 70% utilization, then that is hurting your credit score. If you are not applying for credit that month, I wouldn't worry about micro managing it, but if you are going to apply for new credit, I would get that at less than 9%. The biggest thing is knowing when the creditor reports, so you know when to pay it off. I think an easier solution would be to minimize your credit usage a month or two before any new credit inquires.
3.) You should always pay in full, and auto payments are a good way to make sure you don't forget a payment. Read my comment on number 2 about the creditors reporting a balance.
4. A checking/savings account shouldn't be a hard pull since you are not applying for credit. Go ahead and open it now if you want. Even if they did do a hard check, the sooner you get it done with the sooner it will be off your report.
1. I would try to keep the usage down to improve your score, as I said before. Also, you don't have a well established credit history, which is also hurting your score. As time goes by this will go up on its own.
Where did you get your Fico score from? Do you know what credit reporting agency they pulled. A lot of those credit scores use a different algorithm, and your true score could be vastly different from what that website said.
