Getting odd messages on Rover?

Yes, it's good that you reported the first conversation described.

Sometimes people will contact sitters without filling out all the profile info and pictures, because they're using multiple sources, and not confident that they'll find the right match at rover. When the client sends out a message to a sitter or walker, rover encourages them to increase chances of a match by sending to another person, and then another, etc. When details in their profile or message don't make sense or there are deal breakers you want to eliminate, by all means, use the Rover messaging options to ask them questions to clear it p, before setting up or going to a meet & greet.

All that said, a meet & greet should always start at a mutually agreed location. I'd advise to start somewhere visible to the public (whether that's a sidewalk, landscaped road, or somewhere else), follow your instincts as you get to know the person better before going inside their home or inviting them into yours. At some point, if the requested service is House Sitting, you would need to go in their house to see where everything is that you will need for the dog and any areas where you are permitted and discuss house rules & privileges. For your own safety, you can have a friend, who you instruct in advance to wait outside the home for you or remain silent if invited inside, or you can set up a designated check in call time (like 60 minutes after scheduled start of meeting time) with a friend or family member. Some sitters will set up two meet & greets to better know the person (one at a park, coffee shop, or something like that and the second at the home).