If I give you guys a weapon squad (I probably will eventually) you'll be able to add elements from it to squads for missions.
As for calling stuff in, that's mainly something the people in the field will do. Squads will generally be supplied with a radio, probably on the Jr. NCO, and they can call stuff in on it. If you think they need it you could assign your platoon RTO to a squad, he gets bonuses to certain things.
Reinforcements and off-map support are the two main things that can happen during a battle. Reinforcements are 100% random, determined by a somewhat involved system which I'm not going to detail unless people really want to know, I'm keeping your end of the game rules-light. Just know that each side has a support level which I allude to in the mission briefings, which determines how likely they are to receive support. This could be anything from artillery to a gunship to elements from other units. It works hard to capture the fog of war and chaotic nature of the battle. One turn you can be routinely mopping up local VC when suddenly half a platoon of well armed main force VC move in or a sniper you didn't even know was on the map kills your radioman.
You don't have any control over reinforcements, you just have a vague inkling of how likely you are to get some. If you're not satisfied with that, you can call for off-map support using your squad's radio. This is basically a series of rolls based on stuff like weather, your radioman's rep, your squad leader's rep, etc. You can call for artillery, an air strike from a plane, or gunship support. Artillery's pretty easy to get but lower rep squad's are less likely to be trusted with the bigger stuff. Calling for support could get you a big fat no, in which case you can't try again for the rest of the mission, you might find out something's on the way and'll be there in a few turns, or the support could already be up there and you only find out when the clouds start puking tracer rounds everywhere.
Be very careful with off-map support. Most of the missions aren't going to take place in exceptionally large areas and a lot of fire missions will be danger close. Some of the bigger ordnance can cover a very large chunk of the map and you really don't want that shell going short.
Similar to reinforcements, off-map support isn't determined by you, but by the circumstances. You tell them what you want but you can't decide what's available. You might get lucky with a Cobra gunship, or you might get stuck with something shitty.
I'm worried the HQ position is going to be boring. You don't actually really get to do anything. Sometimes big shit will go down and the whole platoon will be in the field, in which case you get some action, but aside from that...
If I add the weapons squad I might just give it to the HQ so he has something to do, although that raises the question of what happens if the commander or weapons squad leader dies...