Can I choose my own hours on certain days of the week?

There is not a way to make your available times different between days.

What I would do is mark yourself available for all times through Rover (under Service Options), but in your profile at the very top, list your actual availability for each day. Otherwise if you only select 3-10, you'll never show up in searches for 11-3 despite you knowing you are sometimes available those times. This may result in you having to turn down some requests, which can hurt your score, but I also think it will mean you'll get more requests and can maybe work with the owner to find a time that would work for both parties.

Also keep in mind that when searching, not all owners will use the time filter, nor will all owners will read your profile. No matter what you do, you may receive requests for dates and times you are not available for, so just communicate clearly with the client and direct them back to the relevant parts of your profile or the search function.

Good luck!

Just be honest with potential pet parents. Accept the Stays that meet yohr availability and decline the ones that don't.