1. How do I apply a texture to only one side of a brush?
2. How do I make a brush with more than six side, like a hexagonal prism?
3. What do the Skip and Hint overlays do?
1)
This guy. Right clicking will apply a texture to a single face, left clicking will simply select a new face and use that texture. Alt+right clicking is a handy tool for texturing around corners as it snaps the new texture to the alignment of the one you have selected. IE you can texture faces on a curve without getting horrible misalignments caused by the texture face direction on the XYZ axis.
2) There are several brush shapes available, as Bloodhound showed. But you can also use this guy:
Clicking the button once will allow you to clip off one side of the line that you apply in the 2d views using 2 points that you can move about on said 2d view. Clicking it a second time will change the side of the line which gets clipped. Clicking it a third time will clip the brush in two, without deleting one of either of the sides, leaving you with 2 seperate brushes divided by your cut.
3) Typing in "tools" into the texture browser will show you all the special textures that are for use in Hammer and play unique roles in your game environment. Playerclip acts as a barrier that is invisible to players and is a "tool" texture. Brushes assigned such a texture become "tool brushes". They aren't disdinguishable in the 2d views like solid entities, but are differentiated by Hammer all the same. Hints and skips are another tool brush and are used to forcibly cut the world volume into smaller cuboids used to define rendering ingame.
To see such cuboids you can load the "portal file" in Hammer which will show you the maps visleafs, post-compile, as blue lines. You can also view them ingame by using "sv_cheats 1" in the console to enable developer commands and then "mat_leafvis 3". You can also use "1" and "2" to see other visleaf view modes.
