I want to make lids to a box or detach a rectangle from a wall to be a door aka detach an edge by ripping.

Select said edge and rip via V key.

Watch this: http://www.youtube.com/watch?feature=player_detailpage&v=K8RlSiNBsVg

How do I Vertex Paint?

You be patient and watch this nice lady tell you about it. http://www.youtube.com/watch?v=qqoFIvJXJrs

Fixing Normals a.k.a. Why do some of my faces look transparent?

Ctrl + N that fool to make Normals Consistent.

Select a loop a.k.a Double LMB in Maya

Alt + RMB while in Edit Mode. Link: http://wiki.blender.org/index.php/Doc:2.4/Manual/Modeling/Meshes/Selecting/Edges

Instantly switch between Vertex, Edge and Face selection while you are in the edit mode.

"Ctrl+tab 1, 2 and 3. Come on man, it is in the menu if you look." -A guy who reads the manual before he does things.

Link: http://blenderartists.org/forum/showthread.php?213343-Keyboard-Shortcuts-to-switch-to-vertex-edge-face-Select-Mode

Reset/Replace the pivot point of a model.

Put the 3D cursor at the location where you'd like the object center to be. 
Put blender in edit mode(TAB), select all the vertices(A), and then press (Shift+S) then select Cursor > Selection, that will put the cursor at the very middle of your selected vertices.
Go into object mode(TAB), and press the 'object' menu, located at the bottom on default layout, while in the 3D view and select Transform > Center Cursor.

Taken from and edited: http://blenderartists.org/forum/archive/index.php/t-153105.html