Do we need to register with HMRC for that kind of contract?
Yes, you are an employer, they are also likely to have another job so you have to operate PAYE regardless of the pay level.
Assuming you want the person turning up 5 hours a day and not just turning up whenever they like, or supplying someone else to do the job, than it's not really a self employed job.
Some agencies will employ the nanny, operate the PAYE and subcontract the nanny to you. That could suit you. See www.nannytree.co.uk/ for an example of an agency offering that service.
What hourly pay range is reasonable to look after 1/sometimes 2 children? Gross v Net?
Number of children does not affect the salary of a nanny. Nannies are paid per family.
Location would be a factor, places like London can be a lot higher than places more rural.
Given no location provided... I'd guess you are looking at £8 to £13 gross per hour as ballpark figures.
Agree a Gross wage... you have no idea what their tax code would be. They are likely to have another job.
What paid holidays should we offer (there are a lot of bank holidays coming up so would these be part of holiday allowance or on top)
See Casual Workers
For every 10 hours worked : (12.07 ÷ 100) x 10hours = 1.21 hours
So for every 25 hours worked: 3.02 hours of holiday.
Bank holidays are included, so you could ask them to use up the holiday hours on those bank holidays.
Finally, do we have to pay sick leave and/or have other employer issues to consider?
It is normal for a nanny contract to stipulate that it is Statutory Sick Pay. So no sick leave included. See Direct.gov:SSP Entitlement to it is affected by the employees National Insurance contributions - "you must have average earnings of £97 a week before tax and National Insurance contributions are deducted. Your average weekly earnings are calculated over the eight weeks before your sickness began."
As a small employer you may be able to claim back SSP paid out, I can't quite work out how this works but details are here and this is also useful as it is about funding statutory payments.