wow that's a bit tricky. is your nanny the very old auntie type? 40-50 yrs old?
1) if you pay her begining of a month, probably last day you can tell her you have no wish to continue. that's quite harsh but then if there's conflict between her & you, then you wont want to give any chance she sabo your baby.
2) inform her 2 weeks.
3) it's up to you in giving a reason, tell her too ex so you're not continuing. or dont say.