1. Yes, but you do run the risk of not getting what you want. I did several trips this way before settling down to planning ahead, having a better idea of where I wanted to go. I had a bad experience in Inverness (although it was because I was a single--no one wanted to give me a double room), and once could not get a room in Dumfries because an AA convention was in town! A shame, the pubs would have been nice and quiet. I usually travel in October, maybe late September, and haven't had too much trouble. Be aware that some attractions close at the end of September, and many more at the end of October. If you're going to do this, try to get into whatever town you want to stay in by 4:00 at the latest, and make use of the tourist office. They will find you a room for a modest fee--usually a pound or two (I think it was three in Inverness...what's with those people?). There's nothing more disheartening than walking around knocking on doors at 7:00 or 8:00.
2. Yes, but for god's sake
don't! You'll see everything, but you won't see anything. For ten days, I would strongly recommend that you stay three nights in three places, and see those places well or make day trips out of each. If you feel you must wander, book a couple days at the front and at the end of your trip, and have a realistic idea of where you will go in between. Or pick two regions and spend four or five days in each--e.g. Speyside, west coast, Borders, Glasgow/Edinburgh, etc.
My first trip was seventeen days, and I had no idea whether I would go again, so I crammed in a lot--Edinburgh, Orkney, Lewis. Fortunately I have been back seven more times, and of course had to go back and do all those things right! I still go back to some places and find more to see. Far better to pick the few things you want to see most and concentrate on them than to try to do everything.
3. B&B's generally run from £25pp on up. Sometimes you will find bargains, especially in remoter areas. Low-end Hotels start at £30pp, generally. These are about the floor--if you are wandering, be prepared to pay more, as lower-priced rooms may be booked. Also, rooms in the cities will be more.
Start with the Undiscovered Scotland website--
http://www.undiscoveredscotland.co.uk --it's a great resource for things to see and do, accommodation, and restaurants and pubs. Also the Scottish Tourist Board (
http://www.visitscotland.com). The more research you do ahead of time, the more successful your trip will be.
That said, some of my best memories are of the spontaneous, like the time I wandered into the Crask Inn, in the middle of bloody nowhere. There was a house across the street, where the innkeepers lived, and not another for nine miles in any direction. And the pub that night was jumping! The generator went off at midnight, though.