Unfortunately the cat would go against virtually every health and safety reg going. 
Here's what I know from my boss who owns a few cafes/ bars and having worked in some myself:
Your dishwasher would be on permanently.
If you sell anything chilled you need to be taking and recording temps a few times a day because this is a legal requirement. There are a lot of rules around storage etc of food, unless you are selling pre packaged stuff with a load of preservatives in.
You have no control over who comes in , and even in a quite 'naice' part of town you will have people sitting for hours nursing one cup of coffee/ using your electric for their laptops. It can be awkward to move them on when you need the seats for customers who want to spend actual money.
You may have homeless people in begging from your customers. This particular problem is the name of our lives in London.
You will need staff, unless you plan to run it yourself and not take holidays. Or operate very short working hours. This reduces your ( already small) profit. You will need to pay their tax, national insurance, holidays and sick pay.
I'd you have loos, be prepared that everyone and their wife will want to come in and use them without necessarily buying anything. And that you will have to clean them.
Cafes make very little money. You have to sell A LOT of tea and coffee to turn a profit.
Sorry to be a Debbie Downer. I'd keep it as a lovely fantasy