1) Can any unit be a Headquarters unit, even Land Ironclads?
Yes. Any unit can be an HQ unit.

2) Can contraptions ram other contraptions and/or Land Ironclad?
Yes in the sense that that is what they are doing when they engage in Melee combat with other contraptions or LI. However they don't get the ramming attack on the move (p17 of the rules) that LI get - they just ain't vast enough.

3) What is the cost of a mobile supply unit? Should I just cost it out using the point system, applying the appropriate restrictions?
Just add it up using the points system

4) One situation for unit support in melee states that you have to have a friendly unit on both short sides. Is this correct or can you have one on either side?
A unit needs support on BOTH its short sides - being the unit at the end of the line is a lonely place.

5) A unit can shoot at an enemy unit that has moved into melee combat with it this turn (assuming it has not shot already). If this unit is Infantry I would assume that it would not be able to participate in the melee phase. Is my assumption correct?
No, it still gets to fight in Melee. Everyone in Melee combat fights in the melee phase.

6) Fortifications, are they mostly used for scenario? Since deployment is from the table edge (no deployment zones given) we were not sure how to place fortifications.
Yes, in competition-style line-em-up games they should be deployed on the table edge. Scenarios can have them anywhere.

7) The rules state that Underground terranef units move the full rolled movement distance. Since they are modified Land Ironclads this statement ignore the normal movement restriction placed on Land Ironclad although it would apply if they were above ground. Is this correct? Assuming it is correct, then if the underground Terranef has a move of 4 and you roll a 5 does it move 4 or 5 inches?
It'll move 5 inches. The Speed value refers to its speed above ground. Below ground it just chugs away at d6 inches per turn.

If a unit has hits but not enough to destroy the unit outright it can either:
Stay where it is, but keep the hit tokens until next turn and must roll equal to or less than its Command value or be destroyed;
or:
it can fall back 1 inch and lose the hit tokens.

The problem with falling back is that it breaks up your line and makes your forces (very) vulnerable to melee combat and to concentrated shooting in the following turn.