Help with booking/cancellation situation?

So, bit of a strange situation that I'm hoping to get some opinions on...

I went on a meet and greet this afternoon. The client messaged me about a request for May and asked to call me to discuss the dogs and their needs. Normal enough. At the end of the call, he wanted me to do a meet and greet wtih the dogs today, and I happened to be free so I went.

While there, it was definitely a little odd, but nothing that outright made me uncomfortable. The house was just a messy and he was really into talking politics, but he's an older man and I just chalked it up to him being a little kooky. At the end of the meet and greet, he told me he actually needed someone for a few hours next Sunday, which I thought would be a good "practice run" for the longer trip in May. Afterwards I went home and we booked for a drop in this Sunday.

After this booking is where things got a little weird - first he complained about the price of the drop in (which was already really low given the fact that I was only charging him for a 30 minute drop in), then he insisted on me figuring out what card of his was charged by Rover, and then he proceeded to call me despite me politely telling him that I was out and unavailable. He's continued to message me since, asking questions that I've already answered several times.

So, now the overwhelmingness is starting to make me think that the "kookiness" I downplayed at the meet and greet is actually more than him just being odd, but I'm wondering if it's even worth me reaching out to Rover Support to cancel the request or reaching out to the client to see if he would cancel. I know the likely best option is to just follow this one through and not rebook, but I'm a young, single woman trying to go with my gut, and I just want to make sure I'm safe.