Water: "Can we drink tap water on Naxos?" - Yes you can but Naxos has had a drinking water shortage in recent years due to the lack of rain. the local government has resorted to sea-water distillation to tackle the island's water needs. So yes, tap water is drinkable but please use water responsibly.
Internet: "Is internet fast on Naxos?" - Yes, there is broadband internet and more recently fibre-optic internet infrustructure was installed. However, note that during the busy peak summer months when internet use across the island is heavily increased, speeds will be affected.
Here is a list of important and useful telephone numbers for Naxos, Greece: