Well, it all depends on where you want to go. Each region has their own attractions.
Without knowing specifics, I can only give you some general tips.
Or is it maybe an idea to sleep in a tent (don't know if this is allowed and where you can stay, if it's warm enough during nights, ...)
There are plenty of parks that you can stay in with full service camp grounds.
http://www.pc.gc.ca/en/index
If you prefer to rough it, you can. You can ask local tourist bureaus for more specific information. The general rule of thumb is stay off private property and you'll be fine. Will it be cold? I'll put it to you this way, I live in Quebec and I turned the heat off last month.
Do we need to book all our nights or are there enough free rooms during the summer?
All depends on where you are going. Banff..yes. Some out of the way place, probably not
Renting a car? Book in advance, and you must be 25 years of age or older. In most provinces your foreign license is good for about 30 days.
Places to definitly (not) visit?
Stay the hell out of New Brunswick. Seriously, don't even think about it. I spent some time there, its awful. You'll be stepping back in time and the place is hideously expensive.
If your planning on coming to Quebec. Try to speak a little French, the Quebecois appreciate it if you try. They'll laugh and switch to English, a lot of them speak it or at least understand it.
Driving in Quebec is an adventure.
BC is beautiful, but really expensive.
Newfoundland, the same.