1. You can stack divisions up in piles and move them about, still. Or you move them individually. You can also click on an HQ counter, then on that HQ card there'll be a green horizontal bar that separates the HQ itself from the other units attached to it. Clicking on that green bar selects the HQ and all its subordinate units. You can give orders that way.
The command structure is one of the features I like in HOI3, but ymmv.
It's been forever and a day since I played HOI2 or any of it's offshoots so I'll probably be a bit off on the "just like in HOI2" or "different from HOI2" parts, so keep that in mind.
The chain of command is referred to here as the OOB (Order of Battle) just so's there's no confusion. Just like in HOI2, your generals have both traits and skills. In assigning your generals, each plays a part.
At Theater HQ level, skill level reduces overstacking penalties for your units engaged in combat. At Army Group HQ level, skill level reduces supply consumption for all units assigned by 5% per skill point. At Army HQ level, your divisions get an org boots per skill point. At Corps level, you get a boost in how quickly and effeciently your brigades will rotate into battle from reserves (reserves being brigades that don't fit into the "frontage" limit which is 10 for the first province from which the attack originates plus 5 for each additional province that units attack from into the same battle. Frontage only applies to "line" units such as infantry or armor. At beginning, each armor brigade takes up 2 frontage. There's a tech in Land that you can research that reduces that to 1 so you can get more armor brigs into a battle frontage.) Frontage and overstacking are two different issues.
Then there are traits. At division level, traits are 100%. At each level up from there they reduce by 50% iirc. It still adds up though.
When playing a large nation such as Germany or Russia, the OOB is a nifty device to reduce logistics needs by stacking the OOB with Logistics Wizard traited generals (except at Army Group, where higher skill level does best... unless you have a 5+ skill level general AND Log Wis

) In HOI3 there's no Transport Capacity. It's all about supply flow and it gets tricky to manage. There are many threads concerning supply and its management. Those do a much better job of explaining than I am able to do.
2. Leadership Resource is something you manage on the tech research page with sliders. You decide how many leadership points you want to put into diplomacy to create diplo points that allow you to do trades and other diplo things, espionage which allows you to do spy things by building spy points, research by building that pool, and how many officers go to your officer pool.
Officer pool is important. Every time you make a new unit, you use up some officer pool to command that unit. If your officer pool gets below 140%, you start to build up penalty to your attack delay. I don't recall the formula though.
3. In this game, you make divisions from brigades. The combined arms bonus is at division level. There are some very good threads on the division creation issues. I barely understand all the ins and outs myself so wont try explaining it.
4. I suggest getting a grip on the basic game first. Then value add through the mods after you fully understand the game. But Black Ice is one lots play. Myself, I'm still trying to figure out the base game lol.
Edited to add:
Here's the new wiki page:
http://www.hoi3wiki.com/Hearts_of_Iron_3_Wiki
The "quicklinks" in the gray bar at the bottom of the page has links to info that will answer most of your questions much more fully and accurately.
Also:
http://forum.paradoxplaza.com/forum...Restructuring-Tool-for-Hearts-of-Iron-3-(ART)
http://forum.paradoxplaza.com/forum...my-Organizer-A-Full-Feature-Visual-OOB-Editor
Those are two saved game editors that make creation of your OOB much easier if you're playing a large nation with a big military force.