You are allowed to say no! Your body, your baby and all that. I would put money on your body having slowed down because you aren't comfortable with her. Birth is such a psychological thing that (in my experience, at least) you won't relax and get going until you feel it's safe to do so. To the extent that I had two things left to do on my list with DC2 and as soon as I had ticked them off, he came. My DM was a midwife and tells the story of when she attended a home birth. The mother had been in labour for a while but wasn't getting anywhere. Her MIL was there and being very 'helpful'. My mum sent MIL off to the shops and labour started up good and proper!
Sooo, back to you - well done for getting so far. Sorry, I may have missed it but why are you getting induced? You are absolutely within your rights to refuse to have your waters broken. They are acting like a cushion for both you and your baby. Yes, that may be slowing labour down but once they go, chances are things will get more painful much more quickly. The Dr wanted to do an ARM with my DC1 as I 'wasn't progressing' but we said no (because I was, just slowly) and baby came a few hours later. Turns out Dr had been on call since the wee hours and just wanted to go home (not in the UK). I had three home births after that.
Once they break your waters, you're on their time scale and will have to deliver within 24 hours (usually). Now you are much freer to go with the flow. So I'd say (with no medical training and obviously not if there's any medical reason indicating otherwise) to hold off, as it sounds like you want to. First babies take a while and being slow is absolutely fine. If they're properly worried about anything, it won't be a discussion. And her not telling you what the beeping is, is terrible. I'm not sure how big the maternity ward is but you can always request a different midwife (if you're brave enough to ruffle a few feathers). You only get one first birth - stick up for yourself (and get DH to as well). I want to be there! Not in a weird way 
Oops, sorry - up feeding DC4 and got carried away. He's one so cluckiness is returning. Might go and look at photos of puppies or something.
Have a GOOD birth! Hope you're having a quick snooze.