NFHS question on playing shorthanded

[Tru_in_Blu]

First, some NFHS references:

Rule 4 SECTION 3 FORFEITED GAME
ART. 1... A game shall be forfeited to the offended team by the umpire when a team:
f. cannot provide 9 players (FP) to start the game.
g. cannot provide 8 players (FP) in the batting order to finish the game. An out is called in that spot of the batting order (7.4.1). If that player has safely reached base, then the most recent batter not on base is allowed to run for that player, until that player is put out, scores, or the half-inning ends.

Rule 7 SECTION 4 BATTER IS OUT
ART. 1... A team is playing with one less than the starting number in the batting order and her turn to bat is reached.

Rule 2 SECTION 7 BATTING ORDER, OUT OF ORDER
ART. 1... Batting Order. The batting order is the official list of starting offensive players presented in the order in which they are to bat and recorded on a line-up card.

At an apprentice class we recently had a discussion, based on NFHS rules (some of which are referenced above), if a team could play defense with only 7 players.

NFHS does not have a shorthanded rule as ASA does where a FP game could be started with 8 players. NFHS does allow for a team to continue to play with 8 in the batting order and provides an out when that batting order position is due to bat.

Our question is as follows...

During the course of the game, visitors team has a player leave the game due to injury. Whenever that player's turn in the batting order came up, they had to take an out.

In the top of the 7th inning, visitors are ahead. During their offensive half-inning, another player was injured on a play at the plate for the third out of the inning.

Can the visitors take the field in the bottom of the 7th with only 7 defensive players?

If citing any of the previously noted rule references, please explain your logic.

If there are other references that might/do apply, please note those.

A related, but separate question: If a player leaves the game due to injury, can she return to the game later, perhaps even after having had an out called in her batting order position?

Thanx.