Does it cost to adopt a pet

If you can't afford it, let them know. There are programs, including the "Empty the pound month". Adoptions can be subsidized this way. I believe cats are very inexpensive to adopt. Small dogs, I believe, are adopted by lottery.

Yes. But its worth it.

Yes, depending on which type of pet you're looking at will determine the fee.

Yes. I know for dogs it it varies some are $ 50 older ones are $5 I think the fees are listed on their website