Hi, you can find out by google search "beaches-of-koh-larn"

Yes, you can. You can also buy it from the many shops on the island.

There are regular ferries all day to Koh Larn, so you can go there from Pattaya anytime after you arrive.

Teian beach 🏖

The beaches are great on the island. You may take tuk-tuk or moto taxi or rent a bike to get there. Rent costs 300 per day. It takes 20 minutes to get to any beach on the island from the ferry. Ferry can arrive at different places from mainland. But it doesn't matter. There is a transport everywhere.

30 minutes.

I find hiring a motor taxi is the cheapest option

Kho larn is a tad expensive if I were you find a hostel in pattaya and there are many near walking street, that is where Bali hi pier is, and catch the ferry everyday, but rent a motorbike 200 bhat per day, when you get off the ferry walk past the guys who are renting bikes go to the end turn left there is an old woman there renting bikes 200 bhat with gasoline all day, then explore the island, great place.

Most of all the bangkok tour packages includes the Bangkok city tour and Coral island tours. I would suggest if you are in India, to look for "Dpauls " packages as they give variety of such tour packages and even customize. A little on higher side as they generally give better hotels than rest, though they still have the star category mentioned. I would suggest in bangkok you can look to visit the golden Budha temple( sleeping budha), and also the Bangkok king palace. its nice when you are with Family and something to tick mark when you are there. Though these things if you have time, you can ask your hotel travel desk only and they also can arrange, typically a half- to full day trip. Bangkok City tour i think also covers one of them. When you in Pattaya, any hotel that you stay can and should guide you to coral island tours, generally that tour includes parasailing and maybe snorkeling/ banan boat and coral island as a package. . generally around 1500- 1900 bahts( 4000 per person). But since you are with family, i suggest to book the packages from here and maybe few good travel agents can give the above, most of them have what you indicated with a plus/ minus of few things.