I can't imagine that whoever is paying for the childcare is going to accept paying for a nursery space and paying a childminder. (I assume that 5 sessions are funded anyway.) I've had a similar situation, and they would only pay for the hours that the child attended (no holidays, sick days).
Who would be paying the bill in the holidays?
I think that the only way I would accept something like this job would be if there were set hours (eg. 8am-9am and then 3.30pm-whatever).
If I was able to take someone else on during the nursery hours, then I wouldn't charge the student mum, but she would have to take responsibility for child's sickness, having to collect from nursery if sick etc.
If I had to have responsibility, then I think I'd want paying a very decent amount of money to make up for the fact that it uses up a full-time space - not sure if I could be that generous and charge anything less than full-fee.
I guess that depends on how much work there is in your area. How would you feel if you agreed half-fee with the student mum, then someone calls you tomorrow with a full-time mindee that you would have to refuse?
As she is not asking for set hours, and you might have to collect earlier sometimes, I think you need to be very clear as to what you will accept (both financially and with regard to who has responsibility).
Re. putting info in register - if I am being paid but child does not actually come to me, I put in the paid hours in brackets, but also write somewhere why child is not attending (off sick, picked up by granny, going to after-school group etc.)
Phew, that was a long one - sorry!