The bathroom situation depends a lot on where you're travelling. Most cities in Europe have some kind of public facilities (a lot of times in train and bus stations, sometimes in underground uh, buildings.) Usually you have to pay something to use them, ranging anywhere from 10 cents to 1 Euro usually. Big department stores and shopping malls generally have restrooms and you often don't have to pay, but smaller stores are unlikely to let you use theirs (unless you have a small child with a particularly desperate look on their face with you). Restaurants generally reserve their loos for their customers, sometimes you can pay to use them, though. McDonalds (for all their global bad rap) generally have the cleanest "public" restrooms I've seen while travelling - you can either pay or, if you buy something there, you get a code which lets you in for free. (And you can opt just to buy a bottle of water, if the prospect of eating something from McDonalds is too horrific for you!) Bottom line, be sure to always have a pocketful of loose change, in case of need.
In eastern Europe, Asia and Africa (possibly other places as well, these are in my experience), don't be surprised if the toilet you paid for is in fact just a hole in the floor. If you're heading that way, start practising squatting now! My balance improved considerably in Korea.
As for losing weight, I certainly walked off some body fat in three months' travelling - I'm sure it will depend on how much walking you do and what you eat! Don't purposely diet or starve yourself on the road, though, you'll need a lot of energy for getting around, and you wouldn't want to get run down and sick.