a1 and b1 (players) commit a double foul. can a1's part of a double foul be flagrant while b1's part be common?

#1: if so, what would the penalty be?

#2: would b1 be awarded 2 ft's and the ball?

#3: would the ball be opposite the table or at poi?

#4: if team b was in possession of the ball, would the shot clock reset?

Yes.

Penalty: No FTs. A1 is ejected. Ball goes back to team in control with no reset of shot clock. If no team is in control, go to the arrow and reset the shot clock. Ball comes at designated spot nearest to where fouls occurred (neither opposite table nor POI).

See 10-23.e.4 and the chart on page BR-154.

lotto:

what about if you have a double foul and one part is intentional?

Hey Lotto, Care to reconsider that answer?
BR-75 RULE 4-23/DEFINITIONS
Art. 2. Common foul. A common foul shall be a personal foul that is neither flagrant nor intentional, nor committed against a player trying for a field goal, nor part of a double, multiple or simultaneous foul.

I'm just nitpicking the terminology here because Lotto obviously knows this since he correctly told you what happens when a double personal foul is called and A1 did something that was flagrant:

BR-152 RULE 10-23/FOULS AND PENALTIES
A.R. 22. One or both foul(s) of either a multiple personal foul or a double personal foul is flagrant. RULING: For a multiple personal foul, one free throw shall be awarded for each non-flagrant personal foul and two free throws shall be awarded for the flagrant personal foul. For a double personal foul, no free throws shall be awarded. In either case, any player who commits a flagrant personal foul shall be ejected.

BR-153 RULE 10-23/FOULS AND PENALTIES
e. No free throws for:
1. Each common foul before the bonus rule takes effect.
2. A player-control personal foul.
3. A team-control foul.
4. A double personal foul or simultaneous personal foul, even when one or both of the fouls are flagrant or intentional.

BR-154 RULE 10-24/FOULS AND PENALTIES
Section 24. Summary—Administration of Double Fouls
Foul: Double personal foul
Penalty: No shots
Resumption of Play:
Award to the team in control at a designated spot nearest to where the fouls occurred with no reset of the shot clock
(In all other cases, use the alternating-possession arrow with reset of shot clock.)

Terminologically speaking, you're right. A double foul is a single entity, not two separate fouls that can be common or flagrant.

No FTs on any double foul no matter what. Same penalties as above, but no ejection.

The NCAA should really change this. IMO, it is a loophole that fails to punish an intentional foul properly. A1 does something that is considered to be an intentional, while B1 commits a normal foul and both get the same penalty. Hardly seems equitable.

It is probably that way though because it is a one in a million play.