Well first the common bike recommendations:
Giant STP
Kona
Specialized P series
Eastern 26 bikes
To answer your questions
1) Geometry: The main thing I know about this is that you want a chainstay that is pretty short, this is a generalization as their are other factors such as bottom bracket height and other factors. But the shorter the chainstay the easier it is to manual but if it is to short you will be looping out alot etc. Others will chime in with more tips
2)Parts: Their are many parts if you are building up a bike (I found out the hard way but with the help up of atomrcrkhsbiker and a few others I successfully built up my first bike...
Here's a list of all the parts that are needed
Frame:
Fork:
Headset:
Handlebar Stem:
Handlebar:
Grips:
Brakes Lever(s):
Brake(s):
Brake Cables:
Seat:
Seattube:
Seat tube clamp:
Crankset:
bottom bracket (if the crankset does not come with one, make sure the bottom bracket will work with the frame):
Pedals:
Chainring:
Chain:
Cassette:
Spacers:
Chain Tensioner:
Wheels:
Tubes:
Tires:
This looks daunting but by browsing through the show off your bike thread you can find many popular and reliable parts...Just use the search for help if possible and then ask if you can't find anything.
3) Single speed is better as their is less parts to get caught and snagged, etc. Their is a post on here explaining everything needed for singlespeed.
4) Matter of preference many people run disc brakes on mountain bikes but either or
Hope this helps!! Happy Trails!