Do most nannies already have the first aid part?
Yes, they should have First Aid training. For Ofsted approval, it now needs to be a 12 hour course, and must be less than 3 years old.
Best to check with candidates. First Aid I feel is something that the nanny should be keeping updated (every 3 years) and pay for themselves.
Also would I have to inform my house insurance company that I was employing someone on in my home?
No, it is not usual that you would have to specifically inform them. Do check your policy though, to make sure it covers you for an employee and also if there is any particular procedure your insurer requires you to follow.
Talking of insurance, your nanny would also need public liability insurance. The nanny must pay for that themselves, otherwise in the event of a claim, the policy may be invalid. Many nannies do now have insurance, but again it's something to check with candidates.
As you are only needing a nanny for a one or two afternoons (hope I have that right), you should be able to use the Simplified PAYE system for doing payroll. Max limit is £160 a week, thus I expect you can use it, as you would be paying less than that, I'd have thought.