Hi Margaret,
Both reasonable simple processes.
NIE can be obtained from Torrevieja,the last time i went it took 20 minutes to get it processed and then the clients signed an authorisation for me to pick it up in ten days,you don't have to have a property to buy or rent in the pipeline to obtain one.
If you want an instant NIE this can be obtained at Alicante,you have to go early but again the last time i went i had the Cert in my hand by 12 o'clock the same day.
You can keep your car on UK plates up to 6 months without being asked to change over but it is advisable to get them done very soon after applying for your padron or else you may be levied with a 12% import tax charge if you leave it too long.
It should cost you between €600-€800 including the headlight change dependant on the marque of the car.
Many moons ago i brought my UK car over here and did the portsmouth-Santander crossing,1.5 of the most boring days of my life!i wandered from bar to bar passed the same people in the same chairs hour by hour watching cornation street and they were on a mini cruise!!!!!!!
Once you get off the ferry the drive is great through the north of Spain towards Madrid and finally down to Alicante,it took me about 7 hours.
Hope this helps
Georgia