According to Mordenkainen’s Tome of Foes (p. 38), in the "Dreams from Beyond Memory" sidebar: Yes, elves can sleep, but find dreams to be mysterious and weird so they generally choose not to.
Elves can sleep and dream just like any human, but almost all surface elves avoid doing so. Dreams, as humans know them, are strange and confusing to elves. Unlike the actual memories of one's primal soul, present life, or past lives, dreams are uncontrolled products of the subconscious, and perhaps the subconscious minds of those past lives or primal souls as well. An elf who dreams must always wonder whose mind these thoughts first arose from, and why. Priests of Sehanine Moon bow are an exception: they sleep and dream to receive signs from their god, and elves consult such priests to interpret their own dreams.
RAW - No, Otto's Irresistible Dance is not a Charm spell
It does not say that the target will be "charmed", and the condition it imposes is significantly different than the description of the "Charmed" condition.
OID:
A dancing creature must use all its movement to dance without leaving its space and has disadvantage on Dexterity saving throws and attack rolls. While the target is affected by this spell, other creatures have advantage on attack rolls against it.
Charmed:
A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects. The charmer has advantage on any ability check to interact socially with the creature.
A dancing creature can attack the caster (with disadvantage -- and that disadvantage applies to any attack, not just against the caster) and can cast AoE spells that include the caster and anyone else they choose in the target area with no penalty. They just can't move freely. A charmed character can move freely but can't attack or target the caster.
Furthermore, if it were a Charm spell, it would not be necessary to specify that "[c]reatures that can't be charmed are immune to this spell." That appears to be listed as a special exception.
RAI - No, Otto's Irresistible Dance does not impose the Charmed condition
Jeremy Crawford has tweeted saying:
Being charmed means being subjected to the charmed condition
Since OID does not impose the Charmed condition, the Fey Ancestry resistance to "being charmed" does not apply.
What makes sense?
Webster's dictionary says:
charm: to affect by or as if by magic : compel
Magically forcing someone to dance seems to fall completely within that definition.
I would give those with Fey Ancestry advantage on saves against all enchantment spells that compel the user to do something that is not their own free choice. This includes many spells that do not specifically say they are "charms" or that they impose the "Charmed" condition, such as command, compelled duel, and yes, Otto's irresistible dance. I believe those all fall within the common sense and dictionary definitions of "charmed" in this context, and there's nothing in the description of Fey Ancestry that says it only applies to things that grant the "Charmed" condition.
Best Answer
An elf is not immune to the Dragon's Sleep Gas
Jeremy Crawford has clarified in a tweet that Fey Ancestry only protects against magical sleep.
He also clarified in another tweet that a Dragon's breath is not magical.
Unless it is explicitly stated in the Tomb of Annihilation text that this particular Dragon's breath is magical, the effect of the sleep gas would not be prevented by Fey Ancestry.
As mentioned by V2Blast, the Sage Advice Compendium answers the question "Is the breath of a dragon magical?" as below (emphasis mine):