Yes, You can legally do as many inspections as you would like, in accordance with your contract. The contract I have for my rental house stipulates that I will give 72hrs written notice and coordinate the visit with the tenants, but I can inspect as many times as I'd like. Because I am not currently living within a reasonable distance of the rental, my contract also stipulates that I may elect to have an agent of my choosing do the inspection, once coordinated.
It's all about doing your homework before signing the contract. I spent 3 months screening for good tenants and so far I haven't had a single issue. Hopefully it stays that way.
Not true at all in this market. I just listed my house on Zillow (didn't advertize anywhere else) and was getting 3+ inquiries every day for several months. I could have signed a contract in a week if I wanted to.