For getting your rivers right, here's a thread "How to get your rivers in the right place" from the Tutorials/How to Forum.
I'm personally not a fan of rips, folds, curled edges (though I have recently created a old style map with folds), as the map content is the illustration and information needed, not an illustration of a worn map. There's a place for doing that, but for the most part, a map should be providing information to the reader, not showing its wear.
If you're hand-painting all your mountains and trees individually, that's certainly an admirable chore - and you seem to be doing a good job (I like your first attached map, very nice!)
Many of us use map objects - pre-created mountains and forest symbols that are repeated over the course of the entire map, thus each mountain is not unique, but has many copies distributed across the entire map. This way we don't have to paint each mountain one at time. Perhaps I'll create 20 different, individually painted mountains, but with 5 copies of each mountain in use, there are 100 mountains to place (and a lot less work to do.)
Welcome to the Guild, Seredimia!
As a member of the river police, I'd cite you about your unrealistic rivers, but you mentioned your need for this knowledge, so I'm letting you off with a warning (wink!).
I'm also wondering about your roads (I think they are roads) or whatever the swirly brown lines are. Roads should certainly follow the terrain, bypass hills and such, but it seems like the brown lines on the west side of your land go all over the place, yet the terrain looks fairly flat. Your roads should probably be more straight, less curvy.