Internet access in apartments is rare (due to cost mainly) but there are a number of cafes in the zone. Cell phone coverage is excellent.
Yes, I've never had any problem with the phone. Gary is right in suggesting that some cafes provide it (as does the reception area of the hotel) wifi. I assume that if the phone works, a mobile USB stick thing should, in theory, work as well -but watch out for roaming charges!.
I've never tried it, I have to confess. I'm on holiday, and the only purpose the laptop serves during the week is as a music library for lazy evenings on the balcony with a bottle of wine and marvelling at how wonderful the stars look without light pollution.
For anyone who has stayed at the hotel and been driven mad by Miles Davis 'Kind of Blue' being played every night (just loud enough to be heard over the sound of the evening entertainment), yeah, that was us.