This is explained under "Limited Usage" on page 11 of the Monster Manual or here in the basic rules on D&D Beyond:
Recharge X–Y. [...] At the start of each of the monster's turns, roll a d6. If the roll is one of the numbers in the recharge notation, the monster regains the use of the special ability. The ability also recharges when the monster ...
No, holding your breath won't save you
The language of the ancient green dragon's Poison Breath is (MM, p. 284; emphasis mine):
The dragon exhales poisonous gas in a 90-foot cone. Each creature in that area must make a DC 22 Constitution saving throw, [...]
All it says is that there is a poisonous gas, and anyone in its cone is affected. If holding your ...
Gust of wind nullifies the green dragon's breath weapon
I would side with the players on this one.
It is quite clear from the wording of the spell that the "gust" is quite strong. From the description of the gust of wind spell (emphasis mine):
A line of strong wind 60 feet long and 10 feet wide blasts from you in a direction you choose for the ...
The gust causes the gas to vanish in the 10-foot-wide column.
The gust of wind spell lists the following effects, among others:
A line of strong wind 60 feet long and 10 feet wide blasts from you in a direction you choose for the spell's duration. Each creature that starts its turn in the line must succeed on a Strength saving throw or be pushed 15 feet ...
It might also be referring to poison gas traps
Although the example traps in the DMG doesn't include a poison gas trap, there is an example of a poison gas trap in Xanathar's Guide to Everything, under Complex Traps.
It's called a Poisoned Tempest trap on pp. 120-121. This trap has two effects, the first of which is called Poison Gas:
Poison Gas (Initiative ...
At best, advantage.
The poison gas doesn't require you to breath. However, as a DM, feel free to grant the Air Genasi advantage.
Note that poison gas quite often can harm people who don't breath; mustard gas, for example, causes the skin to blister (and not from acid).
Contact poisons exist. This being a dragon... we can assume that poison is poisonous in ...