It's generally not a big deal for either. Being discreet is key.
For #1, A tree, or bush will do. On the other hand, if you're out on the prairies, you'll have to walk a ways off the road.
For #2, it's much the same. However, a small shovel is needed to dig a small hole for obvious reasons. Don't bury the T. P. That can be disposed of when you find a garbage can at a gas station, or park.
Any good book on back country camping and/or wilderness survival, will cover this topic to one degree or another. How To S*** In the Woods, is a good book for #2 Yes... I have the book.
Wikihow has some good articles, too.