The suffocation rules are applicable and clear here, however, you might have to check the errata to get them all. They are as follows:
A creature can hold its breath for a number of minutes equal to 1 + its Constitution modifier (minimum of 30 seconds).
When a creature runs out of breath, it can survive for a number of rounds equal to its Constitution modifier (minimum 1 round). At the start of its next turn, it drops to 0 hit points and is dying.
If you run out of breath, you can’t regain hit points or be
stabilized until you can breathe again.
As stated, they can't regain hit points until they can breathe. They may drink the healing potion all they like, but it will not help them stabilize. It may take awhile for them to no longer be able to hold their breath, but once that occurs, they will die fairly quickly.
Regarding your potion of waterbreathing option, that will fall into DM discretion. If the DM believes that a potion is substantially water, then maybe they can breathe it. Though, I assume if a trap is made out of this potion, then the DM's view is that it isn't water and thus not suitable for respiration.