[RPG] Does the Iron Flask let you Order the Creature Back in Without a Save

(In this case) The Player controls the ordering

Xanathar's Guide to Everything includes an (optional) rule for exactly this situation. On page 77, it contains a section entitled "Simultaneous Effects":

In rare cases, effects can happen at the same time, especially at the start or end of a creature's turn. If two or more things happen at the same time on a character or monster's turn, the person at the game table - whether player or DM - who controls that creature decides the order in which those things happen.

So in this case, Alice's player would control the ordering. Odds are good, he or she would select the Death Saving Throw to come first.

If their maximum hit points is zero then healing magic won't do anything. Healing magic allows a character to "regain" or "restore" hit points, which is always up to your maximum.

When a creature receives healing of any kind, hit points regained are added to its current hit points. A creature's hit points can't exceed its hit point maximum, so any hit points regained in excess of this number are lost.

Basic Rules, Combat chapter.

This disallows cure wounds and healing word and their mass versions, prayer of healing, goodberry (assuming you can feed a berry to an unconscious person) and pretty much all healing potions.

One spell that will help is aid - as long as you keep casting it over and over again.

Your spell bolsters your allies with toughness and resolve. Choose up to three creatures within range. Each target's hit point maximum and current hit points increase by 5 for the duration.

Please note that many effects that reduce maximum hit points also specify really bad things for when the character reaches 0 (for example, the strength drain attack of a shadow). Keeping someone conscious isn't much of an issue when they've turned into an undead monster and are trying to eat your face.