For those of you that fly as a heavy crew

1- if you go with 3 CAs and 1 FO, do all the CAs have to be right seat qualified?

2- Does the PIC listed for the flight have to be in the left seat for every takeoff and landing?

If a 4 man crew is required then the CA flying FO needs to be right seat qual.
Whomever signs for the flight needs to be in the left seat for takeoff and landing

Do any airlines operate double-crewed with three Captains?

How many operate double-crewed with two Captains?

2 captains and 2 FO would be the norm. Otherwise 1 captain and 3 FO.

Most don't have a surplus of captains enough to. put three on one flight. An exception might be line checks and OE.

At K4, if you have three legs in a day or exceed 20hrs we have a LOA that requires 2CAs on those flight. The only time I have seen 3CAs was just a situation that NO FO was legal for the flight. FWIW...ALL CAs at K4 are right seat qualified.

At Atlas the norm for a heavy crew is 1 CA and 3 FO's.

However, things are never "norm" at Atlas. Frequently it'll be multiple CA's on one flight because of scheduling SNAFU's and lack of crews. Whoever signs for a specific leg is in the left seat except for training. All Atlas CA's are right seat qualed.

That's no true - at least at K4 its not
done it and seen it done several times

but the PIC that's signs it is responsible

that said I don't do it anymore - just to be on safe side

Same at Southern. 20 hour duty limit keeps the days a little more sane.

The first issue is whether there is seat dependent training in that airplane, at that airline and how it is defined. That is between the FAA and the airline.

There is no FAR that requires the PIC to be in the left seat. Now you get back into seat dependent issues, company policy and the feelings of the POI. It is even possible for a line check airman conducting OE to be in the jump-seat, though I doubt that anyone has done that since the 1950s.

This is not a subject that can be painted with a broad brush.