Hi!
I'm off to Tenerife at Easter with an 18 and 15 year old, been a couple of times before and would always be happy to return. Plenty for teenagers to do. You could either go to a big family-friendly hotel with day and night organised activities or you could get a self-catering cheapy and go out all the time - all the bars and restaurants are great for families. Plenty of good days out for teenagers - the waterpark, catamaran/dolphin spotting etc. My teens love it.
To answer your questions:
1. It is warm enough to Swim in sea / pools and get a tan - swimming depends on the time of year - if you go in Winter or early Spring then the pools and sea will be very very cold
(unless you go to a very posh hotel with a heated pool) In Summer and early Autumn the cold pool is a welcome relief
You
will get a tan whatever time of year you go - the Canary Islands are much further south than anywhere in Spain or the Med and you
must take high factor suncream and use it often and plentifully.
2. It can be done for less than 2 grand self catering ( we will go to 3 grand if its all inclusive in a nice hotel etc) - Easy! Our Easter trip (all-inclusive) has cost me just under £2k for 3 of us (all priced as adults) and you can easily get a self catering holiday (incl. flights/transfers, the lot) for around £1500-£2k for 2 weeks and there are so many bars and restaurants for eating out, you'll be spoilt for choice.