Yes, they do for pool use only though.
You can buy microfiber ones everywhere along side the beach promenade for around 5 Euros if you want to lay on the beach and don't wont to spoil your travel kg allowances. :-)
Yes they do. The hotel provides vouchers for towels which you redeem by the pool.
Get an answer from Aparthotel Fontanellas Playa staff and past guests.