Point # 1 : It is "Blocking Movement", see below, you have it in the manual :
"Enemy presence (especially Fortifications) inhibits movement in a land region. If this presence is strong enough, your units won’t be able to bypass the defender to penetrate further into the enemy’s rear areas unless they battle and push the enemy back. However, some troops are particularly stealthy and can more easily manage to sneak into the enemy’s rear. This is represented by the Patrol and Evasion Values of the moving and blocking Force’s, as well as by the Military Control exerted over the region.
You cannot enter a land region if the enemy’s Patrol Value divided by your Evasion Value is greater than your Military Control of the region.
Play Note: This basically means you can fall back on friendly regions but are usually prohibited from moving further into enemy territory, unless your Force is particularly stealthy and/or the enemy is lacking proper reconnaissance units.
Patrol and Evasion Values also play a role to avoid combat, if your Force is on Passive Posture or if you have the ‘Evade Fight’ Special Order enabled (see p. 33 and 44).
Procedure: Regions your Force is prohibited from entering will pulsate in red. An icon on the Unit Panel provides you with detailed information".
Point # 2 : Entrenchment is automatically gained when unit doesn't move, but I don't know the real formula.
Point # 3 and 4 , request a better clarification by Pocus.
See this thread also, speaking about artillery :
http://www.ageod-forum.com/showthread.php?t=6624
Point # 5 : It is normal, even frustrating, to avoid keeping Corps integrity too far away from range of the higher HQ army, you won't even be able to re-construct the corps like before loading.
La mort est un mur, mourir est une brèche.