The NIE is free - if you apply in Spain in person at the National Police Station in the area where you are staying all it costs you is your time. This can be considerable depending on where you apply. Marbella for example opens its doors at 9am but unless you are in the queue by about 8AM you will very likely not be seen until 1pm. The department closes at 2pm so one can find that they have queued for a few hours for no reason.
If you want a lawyer to get the NIE for you this they can do by Power of Attorney but understandably they will charge for it - each lawyer's fees vary. If you go to one of the UK Spanish Consulates you can apply there but depends on convenience for you. There is a handling charge of about £30 I think - check out the NIE threads. Clients of mine have had bad experiences with this but apparently the system is now working.
Notary fees relate to three things depending on what you are buying. If it is a resale with an existing mortgage there are Notary charges for cancelling the previous mortgage, there are also Notary fees relating to the property purchase and registration, if you are buying on a mortgage there will be Notary fees relating to the registration of the mortgage.
What you should expect to pay depends very much on what you are buying and how you are buying it so too general a question to answer.
Notaries are the wealthiest people in Spain. A poor one earns in excess of 1,000,000€ a year and that is without the under the table deals that get put their way. Such as bank repossessions and goods seized by the State under proceeds of crime etc. Little bit like a liquidator or receiver they are there to disperse goods and chattels.
Rgds