Way points

Sorry if I am missing something, but how do I connect the small vertical lines to the "main" way path? 

Why have you got vertical lines outside of your way border? You can only connect/disconnect nodes to & from existing nodes by selecting a node & then right clicking on another one, you can't insert new ones, so take that into consideration when you create way system paths. Just delete the long line & redo it so that you have enough nodes wherever you need them to be.

Ah, thanks. But now, a weird thing happens: When I point outside of the way borders, my character still goes there, outside of the borders. Do you know why this happens?

are the path lines going outside of the way border you created?

Yes, but can't I make a way to move my character to the closest point inside of the way border, if I click for example on the wall?

As far as I know, the character will move to the node nearest to the point where you clicked. 

The pathing isn't strict. It more often than not automatically calculates the direct path or nearest point to wherever you clicked. The only time it strictly tends to follow waypaths is when a character needs to walk around a cutout way border section. You need to create plenty of points - as esmeralda said - to allow the engine to calculate the nearest point more accurately. Avoid having the way paths going outside of the way border.