So yes, I've made my visit by now.
First, for sleeping
- when arriving (at 1am) I took a flybus between Keflavik airport and BSI (the bus central station). Then I "slept" there (or I least I stayed there). Plenty of people were doing the same, but it wasn't so great (a lot of movements, not so much room, etc.). The BSI is open all night, with arrivals and departures all night long.
- when leaving (flight back at 6am), I stayed for the night at Keflavik airport. A lot of people were also doing that. A guard woke me up, but I was taking an entire bench to sleep, so I guess it's normal.
Then, to go to Myvatn
I took an internal flight between Reykjavik and Akureyri (~100€), then a bus to Myvatn (~25€) (route 56).
I've hitched a lot in the south and it was globally easy, even if 2 or 3 times I had to wait for 1+ hour (even on the main road). Some other hitchhikers told my that in the north east (and in the westfjords) it was more difficult because there were much less cars, but I think it's still relatively easy. There are a lot of hitchhikers. I was quite lucky because around half of the people giving me a lift were icelandic people (and it's nice to meet locals); some other hitchhikers met almost only other tourists.