Georgie is right. Whilst you’ll get a lot of standard replies about what to ask, the only questions that matter are the ones that really matter to you. So think about what matters to you.
Don’t be embarrassed about asking something that might seem like a silly question. There are no silly questions. Or rather, the only silly question is the one you don’t ask, which later comes back to bite you on the bum because you didn’t ask it iyswim.
If anyone tells you to "go with your gut" you should smile politely and ignore them for the fool they are. Your gut does an excellent job of telling you when you need to eat, poo, or throw up: that’s what it’s good at. Guts are terrible at making childcare decisions. Such an important decision requires a parent to make a mature, informed decision with their brain, using as much information as they can get. So try to see through the appearances, 'personal chemistry', 'magic', rainbows, etc.
It’s worth remembering that most childcare arrangements that break down, do so over money, contract disputes, and divergent expectations. These are all things which can and should be agreed in advance. 90%+ of the disputes I encounter between parents and childcare providers involve a family complaining about something they actually agreed to in the contract. Only a very small proportion break down over standards of care. It is very important to give proper consideration to the childminder's contract, policies and procedures. Be clear on what you expect from your childminder, and what s/he will expect from you.
Don’t forget your child. They may have questions they want to ask. A good childminder will find this input very helpful too.