Well, I believe I can answer the first question...
A Jeep can hold 2 steps, so yes you can put an HMG and the 1st SGT in the same Jeep.
As for the next two, from 7.4.3 in the rulebook:
If a vehicle moves, then any passengers it is carrying are exposed
I believe you place an Exposed marker on the Jeep, which also applies to the passengers. So I don't think an HMG can fire from the Jeep until the following turn when the exposed marker has been removed.
But I'm still learning this game myself