I spent two weeks cycling a bit of Iceland in 2010. I’d love to go back!
We went in August and I wasn’t bitten by a single bug the whole time. I was amazed.
We had a full double wall tent but I slept outside – no bivy or anything - whenever the lack of rain permitted ( which wasn’t too often! ).
Don’t worry about bugs at all. I’d worry about good rain gear! You’re going to need it, along with good base layers that dry easily. Maybe an umbrella? I might recommend a free standing tent as well, with a vestibule you can cook in out of the wind and rain. I don’t know your itinerary but I found lots of high wind, sand and loose soil in the interior which would make setting up a tarp or non-free standing tent a bit of a challenge, but of course not impossible if you know your stuff and as always, look for sheltered spots.
What kind of stove are you using? At the camp ground in Reykjavik we came across a decent supply of half empty stove gas canisters and liquid fuel given away by campers leaving country.
White gas by the gallon and one pound propane canisters can be found in some N1 gas stations. I had a liquid fuel stove that could run on auto gas and used scrounged fuel the whole trip, my buddy ponied up 3,000Ikr for a one pound propane canister for his little “gassy”.
Ah, the food is very good up there, or at least I thought so, but I live on rabbit, venison roasts, goat stew and homemade cheese and home baked bread, so the local sheep stew, yogurt ( Skyr ) and so forth was right up my alley, but I didn’t go so far as to try the singed sheep head. Don’t forget to try the puffin! It is on the endangered species list most everywhere else so it’s probably the only place you’ll get to try it, and once you do you’ll know why it’s going extinct – It’s very good! Try the whale and other sea food, also very good indeed.
You can buy horse meat which is also very good, but I’ve butchered a horse or two in my time so that was nothing new. We bought local food and cooked fancy meals the whole time, it was great.
For fast food, go to the nearest N1 gas station, the food there is also surprisingly good, as is the coffee.
Do you fish? The fishing up there is about as good as it gets!
I wouldn’t worry about filtering or treating your water either, ( but then I never do ) the water up there is as pure and delicious as it gets.
Have a great trip!