Hello Little Seahorse

first of all I am sure that whatever you do you will have a great time! Cozumel is a fantastic island and even more if you are diving.
To go form Cancun to Playa there is a bus just outside the terminal called ADO and it should cost you about 150 pesos (more or less) but if there is four of you I recommend a Taxi which will end up costing almost the same and it is faster. The ferry is only a few blocks away from where you will be dropped off and if you are not too tired I recommend to walk around a little bit on 5th street in Playa del Carmen (but seeing that you are going to the cenotes I would probably recommend planning to stay in Playa and walk around fifth street and maybe get some lunch or dinner there) The ferry is only about 40 minutes long. When you arrive to Cozumel just take a taxi right in front of the exit from the ferry.
Diving wise I would recommend you ask for a local DM because usually big companies like that have a lot of foreigners that don't know the reef very well and that could change the whole experience.
If you can get the group to go to town to get dinner and walk around I highly recommend it. There are some fantastic restaurants all over town.
I see a lot of other people have given you a lot of info but I hope this is helpful to you.
LAst thing, if you want to make your trip from cancun to Cozumel or the other way or even both a bit shorter there is a small local airline that does the trip for around 35 to 40 usd and it is a 15 minute scenic flight. It is worth the extra money just for the view!