When attacking from a region into another region, do supporting units from territories connected to the region the attackers are coming from count toward their total strength? Or is it only supporting units from regions connected to the defender's region?
The following is taken from page 12 of the rules (emphasis mine):
If you move one or more of your units into an area containing units from another house, a battle will ensue once you have completed all your movement from that March order. If you move into such an area, you are considered the attacker, and the opponent currently occupying the area you entered is considered the defender.
Support can only be given to the area in which the battle takes place, and only if you have a Support order adjacent to the embattled area. Since the March order is played out to completion before the battle starts, the only embattled area would be the area that the attacker moved into (i.e., the defender's area). The concepts of attacker and defender don't even apply until after you've moved into this area.
This is explicitly clarified in page 18 of the second edition rules:
Reminder: Support can be granted only from an area containing a Support Order that is adjacent to the embattled area. Do not confuse the embattled area with the area the attacking March Order was assigned to (and from which the attackers marched).