I'm sorry for your loss.
The number of questions you have, and the other questions that are raised by your situation, cannot be answered on a free legal forum. You really need to contact a probate attorney in your area right away. Once the probate proceeding is started and you are appointed executor or personal representative, you will then have authority to collect rents and pay bills, etc. If you pay reasonable expenses from your own funds that are for the benefit of the estate you can seek reimbursement. The bank accounts in both names may or may not be part of the estate, depending on how they are titled, i.e. tenants in common or joint tenancy.
I know this sounds like a lot of ifs and maybes, but that's why it's important to contact a local attorney who can address all of your questions.
First, I'm very sorry to hear about your husband. I think you need to see an attorney as soon as possible. There is a guardianship issue with the 16 year old which needs to be addressed, immediately. Also, the guardian needs to file for social security for the minor. As you've stated the estate needs to be administered. Call the mortgage company and the utility company and let them know that your husband has passed and that you are in the process of hiring an attorney, so that they will know what is going on and give you some time to pay the bills. Rent from the property needs to be deposited in the estate account which can't be opened until the administrative process is started. The money in the joint accounts is yours. I don't know whether your husband had a will or how the money was left, but that will determine how the property will pass and the reimbursement for expenses.