yes, you can park your car in the car park at the ferry port, it is free and safe
no real need to buy your tickets before your arrival you can buy the ticket at the ferryport, even on busy days there is alway plenty of room. I am guessing you will be in the city so you can also buy them there on the day. If you buy on line it is 10% cheaper, than if you buy the tickets in Galway City or the ferryport.
You can rent bikes at the pier in Cill Rónain (Kilronan) for 10 euro a day, or take a pony and trap and or do a bus tour of the island, I think the bus tour is abour 10 euro have no idea on the price of the pony and trap.
You can get a map of the island in the office in Galway or before you board the ferry. I don't know your fitness levels but if you hire bike, that it easy when cycling to Dún Aegus as there are a number of hills and they can be tough.
Apart from the obvious what should you see and do
Teampall Bheanain - reputed to be the smallest chuch in the world, I love the views of uan Cill Einne (Killeany Bay) from here.
Dún Dúchathair - Less famous than Dún Aengus , this massive and impressive cliffside ruin is on the southern side of the island and you get a fraction of the people here, the number of times I've been there, there were never more than 2 other people there.
Na Seacht d'Teampheall - Collection of 15th century churches and monastic houses, great view from the hill.
Dún Eoghanachta - A circular fort near Na Seacht d'Teampheall.
I don't know when you are going but in July and August they have Seó Stáitse (stage shows) in Halla Rónáin, last year they had Aistear Ceilteach (Celtic Passage) which was an excellent traditional song and dance show with a number of local children.
Enjoy!