2006 f350 truck repair.

OK, bear with me on this one for a minute.  I'm kind of new at this.  I own a
2006 F350 4x4, 8 foot bed, 5.4L gas engine.  I bought it as sort of a project
for my son and I and it turned quickly to a nightmare.  I am trying to diagnose
several problems and figured I would see if anyone can help.  

1. There is a severe shake in the truck when driving that gets much worse
when braking.  I have seen that this may be due to several issues (warped
rotors, alignment, suspension problems, etc.)  Where do I start to figure out
what the problem is?  


2. The 4x4 does not engage.  This may be the transfer switch, but could it be
related to the first question?

3. I feel pretting cnfident the suspension is shot.  Its a jacked up truck and I
can feel every bump in the road.  Doesn't seem right.  

4. When I try to put gas in it, it keeps disengaging the pump.  I thought this
was due to the shape of the opening for the gas but was told it may be the
air vent on the gas tank.  Is that the more likely case?

I want this truck to run well for my son and we are learning about working on
cars together.  Been an experience so far...