I am unsure what rules the league was playing under but, FYI:
A team (JO fast pitch) can play with 8, but ASA rule 5-4-J states that if a team is playing one player short and another player becomes ill or injured, leaving the team with two less players than the required number, the game shall be declared a forefeit.
ASA rule 4-1-D refers to the ASA shorthanded rule. JO fast pitch requires 9 to start the game, however, you may start the game with 8. The vacant position must be listed last in the batting order, and an out shall be declared when that spot comes up. ASA rule 4-1-D-2 states that absolutely under no circumstances shall a team be permitted to bat less than 8. (can have one automatic out, but can NOT have 2).
If the player leaving the game is a runner or, in your case, a batter, she shall be declared out. However, more importantly in your case, under ASA rules, if that batter could not continue, since the team was already playing with 8, the game would be over and a forefeit would be declared. So in the first situation, no, it would be a forefeit, not just an out if she could not continue.
In the second case, you should not have allowed a courtesy runner (last batted out) to run for the batter who was HBP. That's an illegal runner.(ASA 4-6-E-3-a). First, courtesy runners are only allowed for the pitcher and catcher and must be a player who has not yet been in the game. Since you didn't have anyone on either side who fits that, due to no substitutes. Plus, if the batter who was HBP was not the pitcher of catcher, then the runner for that player would be a substitute, not a courtesy runner. (CR do not count against the substitution of the pitcher, catcher or CR.) However, in your defense, I know a lot of coaches who try to apply this rule (not sure why). It's not a rule in ASA or PONY, and probably not in most other alphabet leagues.
During the course of the game, you said she missed her turn at bat with no penalty. This is incorrect. An out should have been declared when that player's position in the batting order came up.
ASA 4-1-D-2-e states a player who has left the game can not return to the lineup - when she left the game she became ineligible to return. A return to the lineup will constitute a forefeit if properly protested.
When a team playing with 8 has a player leave, the game is over, and it constitutes a forefeit. The ineligible player can not come back in to play. You are correct that she can not return unless it was due to the blood rule. But you should have asked the league representative what rules they are governed by prior to the start of the game, so you are aware what to call in these situations.
Chalk it up as a learning experience. In the future, I would be sure to ask a league rep prior to my captain/coaches pre-game meeting what rules are governing this league game play. If someone from the league is unavailable, I would "ask" both coaches at the pregame if we were playing ASA rules. If they state yes, then you apply ASA rules during the contest.
* Does this league allow all to bat and open substitutions all the time, or just today because, in today's game this would not become an issue at all?
On edit:
Sorry Dave...it took me forever to type this and when I finished, I saw you had already answered most, if not all, of it.