Hi @Jacob Crow
1. Interest rates are subject to market conditions, and can change daily even. There will not be a wide range on what each bank is offering, it is going to be more based on what the current market dictates. You can go look up what the current rate is for a 30-year fixed now online.
2. If you get a loan pre-approval from a bank, they will need to do a hard inquiry against your credit which will impact your credit score. But as you said if you get multiple pre-approvals within a 45 day window credit bureaus will understand what your are doing and only count it as one inquiry.
3. If you have not signed an exclusive with an agent, selecting an agent is completely optional and whether or not you want to work with one is your choice. Agents create value by assisting and guiding buyers/sellers through the transaction and if your comfortable doing this yourself you don't need to use one. If you do decide to use one it is best to get them involved sooner than later so yes at minimum they should be submitting an offer on your behalf.