Some answers for the Minnesota parts:
Hwy 61 - There is some nasty, the worst of it being near near Silver Bay, despite it being a designated bike route. Try to hit it midweek or off season, lots of tourists in RVs and only the locals are polite. Fortunately most of the road is great, and I've heard the traffic is generally better past Illgen City, which is the furthest I've ever been on bike. Hop on the Gitchi Gami trail where segments exist. I believe 21 miles are actually completed out of 86, so while you'll get dumped out on the road often, it's a nice break from the traffic while it lasts. Paradoxically, some of the worst parts of 61 are between trail segments, whereas areas where you can avoid the road by way of the bike trail have wide, smooth shoulders.
Mosquitoes - Always depends on the year. Generally the wind from the lake will be on your side and discourage them. Stray too far and you'll get eaten alive if it's been hot and wet. I'd say absolutely carry some heavy deet, but don't stress out over it.
Unsolicited advice - This was brought up on another Lake Tour thread, but it's worth mentioning again that the Minnesota state park campgrounds(Gooseberry and split rock especially) often fill up in advance. Most of the private campgrounds are ridiculously expensive. There are national forest campgrounds (Eckbeck or Finland on the Baptism river are beautiful) which are a bit out of the way, but never seem to fill up. If you hang around while folks are being turned away at the park gates, you might even be able to get a ride to the far flung ones. The Marina campground in Grand Portage has some tent sites hanging over the lake, which are usually available.
Oh, and have a pasty or Beargrease burger at Betty's Pies in Two Harbours! Absolutely fantastic.