Sounds like a great plan for a holiday! weeks
I'm lucky enough to spend around 4 every summer in Sweden, near Gothenburg (married a Swede).
So as for the weather, it can occasionally be very hot (28C - 30C), but it can also be very unpredictable, rainy, stormy etc. Think of something like summer in Scotland and you'll have the picture.
Mosquitos can be a menace, especially in dense forrest areas, less so where you can get a breeze e.g. by the coast. So, cover up completely after dark. Make sure your tent / bivvy / hammock has very fine gauge netting. Wear lots of repellant. Eat vitamin B for a few weeks before you go (Marmite will do). the first few years I went I had terrible huge bites, but they are slowly getting less itchy as I build up resistance.
Finance wise, things that are still marginally more expensive include alcohol, eating out, taxis etc. Swedish youth hostels are good (you could use the one in GTB on your return), people are generally welcoming to the English, but just be sensible, don't go chopping down loads of trees in a nature reserve a few Km's outside town, or camping in someone's back garden. Almost everyone speaks good English
Distances are huge as Robin said, so don't bite off too much.
If you need any more specific info I'll try to help if I can. Good luck, + hope you have a great time!