3 ways to get there. 1. Walk from the pier about 15 minutes or so. 2. Take a boat taxi from the pier (I'm guessing 150-200thb) 3. Ride a scooter or rent a taxi. The only method I've taken is to walk. I actually rode my scooter to the end of the road heading south from the pier in the Charm churee resort. Then it was a 10 minute walk from where you park your scooter to sai nuan beach. There was no fee when I visited in 2016. Not sure now. The walk is really fun. It meanders through the little bungalows of the resort, then goes right along the ocean. It's mostly tree covered and has great ocean views all along. Here's a video that I put together. It shows Sai Nuan beach and a little bit of the snorkeling footage from that location starting at 1:58. It actually shows all the beaches I visited on koh Tao. the video is on you tube and it's called "Koh Tao Beach Comparison"

There wasn’t when I went a couple of years ago but there might be now. You’ll get better, more up to date answers if you ask in the general Koh Tao forum

Jansom bay (south west), Sai Nuan (south west), Freedom beach (south), Haad Thien also called shark bay (south east), Ao Leuk (south east), Tanote (south east). All of these have beaches with shallow water up close to the beach and deeper water out farther where the snorkeling get's better. It partially depends on what week you are there according to the tide calendar. If the tide is really low then shark bay and freedom beach can be a bit of a pain to get out to deep enough water for snorkeling.