This is the first Grigsby game I've properly played. I remember dabbling a bit with Uncommon Valor back in the days, and maybe I've played some other title a long time ago.. my first computer was a C64 back in the days and I've been interested in strategy games for a long time. I used to play quite a lot the board game kind, and liked the social factor (when me and friends I still had time to be social from work, family, "proper" hobbies and other silly adult things). Computer games have of course nice benefits like fog of war and more detailed modelling of the troops etc, especially with the current computing power.
Anyways, I eventually managed to win the introductory Sicily scenario after several tries and yesterday I finished my third or fourth try of the Battleground Italy scenario, ending in minor Allied victory. A minor for the Allies perhaps, but a major one for me personally

I think next step then is the full campaign and hopefully some PBEM in the future, but first I have some questions to step up my game and to understand this title better (note that some of these might be somewhat specific to the Italian campaign, as that's what I've been playing. And some of them have probably been asked before, but please bare with me

1. Support Units:
I understand that the support units attached to a HQ unit can participate to several battles in a round (although have to pass a check in order to do take part in any one battle) while ones attached directly to units only participate in battles that that unit participates in. There are also limits of support units which can participate to battle, but is this limit applied if I have for example several divisions, each having three support units and participating in the same battle? If the number is limited, what are the rules for selecting the support units that participate in the battle?
Is there any "rules" for optimally mixing support units? E.g. would it make sense to attach three (combat) engineer units to a division one is using to attack a fortified zone, or should one have move balanced mix of support units (I suppose artillery is good for almost any situation)? Does it make sense to attach AAA units to divisions?
Summa summarum: While I've definitely noticed the benefit of the support units, I'm trying to further understand the optimal use of them.
2. Exploiting breakthroughs:
Any hints on exploiting breakthroughs? I've tried to use my tanks efficiently but very rarely I seem to be able to penetrate deeply (seem to run out of MPs) and then in the next turn the AI seems to be very efficient in retreating out of reach. I understand that the terrain, enemy ZOC, and morale of the advancing troops at least play a role in this...
3. Best practices in rotating troops:
It seems that I end up having all of my units in the front line all the time without any reserves which eventually causes their efficiency to fall. On the other hand, if I keep a reserve to roll fresh troops to the front line, I do not seem to be able to achieve breakthroughs or (related to Q2 above) at least seem to be able to exploit them properly. This ends up me banging on the defence line for a long time with high casualties until something finally breaks. Then the AI retreats a bit and the whole process starts over.
How do you guys rotate your troops and still maintain a strong enough front line for breakthroughs? Do you concentrate your rotation in one point while keeping a relatively thin front line in other places or? How often do you rotate your front line units?
4. Engineers
In the Battleground Italy scenario there are couple of engineer units (regiments?). Do these have some specific use or should they be considered just as general infantry units?
5. Air Operations
What are the negative effects of the area in the efficiency of ground attack, air superiority and recon? Do you like to concentrate your missions on more restricted area or spread the effect more widely and let the AI decide the targets?
I have mostly been using my air force rather conservatively, pumping up the attacks to high intensity and every day of the week during some critical stages of attacks for period of few weeks on the max. Any rules of thumb on how much can one push his or her AF without adverse effects? Should one stick to a "five day work week" for the air units, or push them further?
When and where to move the AFHQs? Do you keep them in close to your front lines or keep them further back? Are there any benefits for bringing them up front?
6. HQs
A bit similar to the second question about air operations: Does it benefit to bring higher level army HQs close to the front?
7. Routing isolated units:
In the situations where I've been able to isolate and completely surround some enemy units, they have sometimes routed and got out of the pocket. This seems a bit counter intuitive, but this might be due to the abstracted level of the map and units and the I-GO-U-GO sequence. I'd expect the trapped troops to be completely annihilated or captured in these cases (mind you, I do not have clear view on how many enemies actually slip out of the encirclement and how many perish in the process).
I think I'll start a new scenario today, so I might come up with further questions, but there are some for starters

P.S. As I had my laptop with me on my holidays and no access to the Internet, I think that the version that I've been mostly using is rather old. Now I'm using the latest version.