Hope you can help me with those:

1. I've searched through the rulebook, but I couldn't find the answer. What exactly defines as a friendly area? How does it differ from control of an area?

2. When a base is attacked and the only remaining unit on the area containing that base is an enemy Assist unit, is the base still destroyed during Regrouping Phase? It seems illogical that units with no attack capability would destroy the entire base themselves, but I couldn't find it either in rulebook.

1. there isn't any difference. when you control an area, this area is friendly to you. so a friendly area is every area you control, that means where you have one or more units or an base/installation.

2. I myself also don't like handle it this way. according to rules the attacker has won, when the defender has no units left after the battle and the attacker at least one. When a area contains a base AND units from another player, the base is destroyed. This does NOT exclude assist units.

maybe you should make own rules when it comes to that point. a air-defense-modul (i hope its called sth. like this in english) for example should make enemy assists units retreat, when they are the only units left after a battle on a base.

you are confusing fluff with balance

Luuna said:

To be more precise - without enemy units/bases installations. Such area would be enemy area (although this area would be also enemy for your opponent) or contested (if a battle is going to be resolved there).

For Assist units - do not treat it like exactly that unit would destroy your base. This happens during Regrouping Phase, if player loses control over the area. How could he keep the base in the area which he no longer controls? It really doesn't matter what units were used by the opponent to gain the control.