I think it’s:
You’re right, whether using the box rules or LHTR. Taking a power’s IPCs by taking their capital is not income, so you can collect it even if your capital is held by the enemy.
If Germany Controls the Suez Cannal, (or panama for that matter) can Japan use it as well?
What if Germany controls Egypt and Japan Controls Persia? Can either use it then?
Yes and yes.
I too have a rule question. Is it true that after you make your combat moves, you can’t move any of those pieces again during the non-combat move phase? B/c I’ve always thougth that you can move them, as well as other pieces, to different territories, even if they were in combat. If this is the case, what’s the reasoning behind it?
Both land and naval units that engage in combat remain in the area of combat and cannot be moved in the non-combat phase. Retreated units have to stay in the territory/sea zone they were retreated to. The only units that can move after Combat (and in fact HAVE to move in almost all cases) are aircraft.
If you need a basis in reality for this rule, consider those forces to be being re-supplied, repared, reinforced, replacing casualties, etc. as well as securing the area, reparing damaged infrastructure (bridges, airfields, etc) during the non-combat phase. For retreated units, consider them to be regrouping, replacing lost equipment, etc.