1. Yes, you will need proff of no claims discount. Your old insurance policy from UK will suffice if it is up to date.
2. Depends on whether it is in stock with the colour/specs you require. Our new one was 6 days but the chap after me had to wait 3 months. The dealer will tell you what models are in stock.
3. Yes, the dealer will register it to you with road tax remaining for the rest of the year. Make sure the fees for this are included in the price which it should be.
4. If you are a resident, you will need residency card, passport and up to date padron (within 3 months). If you are non-resident, you will need up to date padron, passport, NIE and copy of deeds/rental agreement.
Oh, don't forget the money. Also, the dealer won't allow you to drive it away without insurance. Our insurance company e-mailed a copy to the dealer.