Iceland

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I'll be travelling to iceland from western canada at the end of the month for 8 days and i was looking for some advice on the spots to avoid and the things that are a must see while driving around the entire island. I'm considering renting a car and sleeping in it along with camping in various spots. Is there designated campsites? Can i camp anywhere that isn't private property or a park? Is there some kind of rideshare meetup type thing so I can get someone to chip in for the rental and join me for this excursion?

Some rough ideas of things i'd like to get to while touring around the area. I'm down for anything involving the nature of this amazing country, hiking, kayaking, climbing, hot springs and checking out some geological oddities.
DettiFoss
Jokulsarlon lagoon
Westman Island
The golden circle
thingvellir National park
Hverir mud pools
snaefellsnes peninsula

Would greatly appreciate some advice as this will be my first overseas trip and it's incredibly short notice. Was originally going to drive up to alaska but a friend bailed and my car isn't in good enough shape for that type of trip.