Hi, Summer. Here are a few brief answers to some of your questions. This is just what I do so it may or may not work for you. I would call at least one prior landlord reference but you may find they don't respond so you may need to call a few. For travel medical professionals I will accept a copy of their fully executed contract in lieu of pay stubs because their prior pay stubs may be totally different than their current contracted rate.
If you're renting to multiple individuals for the same time period they should all pass the background check and all be signers of the lease. I don't charge an application fee but I do have the tenant pay for their background check.
For pet deposit, you'll need to discuss with them what their plans are for the pet when they're gone. Ideally, they're either going to pet day care or have a pet walker come in to relieve them during the day. But some people do leave them in a fenced yard or even in the home. It just depends on what you're comfortable allowing. Service animals are not a red flag in my book.
Rent is always due the 1st day of the month and late fees apply by the 3rd. Guests are responsible for moving trash and recyling bins to/from the curb and that is spelled out in the lease.
hard to say how many pages the typical MTR lease is. Use a state-specific lease and feave everything in there so long as it applies. You can add clauses, like how to handle garbage and where parking is allowed, but don't take out anything relevant in your state specific lease. I use Baselane's partner Rocket Lawyer to create the lease but I've used Keycheck and Avail before and they're all very similar.