$15 round-trip? I don't think so.
Never buy a round-trip ticket. Now this is a long story, but I'll explain...
PDC to Coz has long had two ferry companies with a non-compete agreement that shared schedules. They charge $10.50 one-way or $21 round-trip so no savings for buying a round-trip - but then you are stuck waiting for that company's boat, as they generally take turns. See
Cozumel Ferry Schedules: Cozumel and Playa del Carmen
The new ferry company is cheaper, 135 Pesos or about $8.50 one-way, they start earlier, run later, and generally run between the times of the other companies. See
https://www.facebook.com/barcoscaribe?fref=photo
My choice has always been
the next one leaving - whichever? Anyway, the schedules at the links will give you an idea of when you can probably go, weather and other variables allowing.
You sure you don't want a rental car? How are you getting from the Cancun airport to Akumal? I have an email contact for a great van guy if you need to arrange transportation, cheapest I've seen and dependable, but back to your questions...
Ado bus is very popular in Mexico but I won't go into detail as they do not stop in Akumal. Akumal is 38 Km/24 miles from PDC so taxi service would be a little pricey, depending on negotiation skills - really, can vary greatly.*
I see on TripAdvisor that Riveria buses run from the Cancun airport to Akumal, pretty cheap at $6.50, and are probably nice:
Akumal: Arriving & Departing - TripAdvisor Getting from Akumal to PDC & back is done on Mayab bus or a
"Collectivo." Mayab bus doesn't have a schedule online, maybe not at all, and the shared vans are pot luck on time & room. See
Where can I find the Mayab bus schedule from PDC to Akumal? - Akumal Forum - TripAdvisor
You really need a rental car, but ask your resort what they know about bus services. For car rentals, I use Easyway with all inclusive insurance.
Easy Way Cancun Car Rental | your Cancun Airport Rental Car
Before I forget, look at Can-do maps. You might want to select the one that seems most helpful.
http://www.cancunmap.com/
I can't suggest any particular dive Ops in PDC but there are many good ones. You can browse the threads here. For Cozumel, the list of great dive Ops is a long one, and again - I'll suggest looking over threads on the Cozumel forum here. For both destinations, I do have a few suggestions that extremely important...
1: Get DAN dive insurance, or Dive Assure. Keep your ID card handy at all times and keep their benefits in mind - including non-diving risks & benefits.
2: For the first 2-tank trip out, hire a private DM. Money well spent to help keep you safe as you learn about boat diving, ocean diving in general, wicked currents that happen at times in the channel there, etc.
3: It still amazes me that I see divers without SMBs & storm whistles. I carry those and more, but always carry those.
If you give more info on your party, resort, length of stay, etc. we may be able to help more.
*For example, my van guy mentioned above charged me $20 from downtown Cancun to the airport last month, but when I first got to Cancun - several hours late after Texas weather delays, had planned to take the Ado bus to town then a cab to my dentist office, I was stuck. Arriving as late as I did, I grabbed a cab - for $60! I was at the airport, needed one then, and had n leverage.