According to the title of this question...
Who needs a dragons
Is it "a dragons" or just "dragons"?
And "need" or "needs"?
A [plural]
Is never correct in any sentence, so the correct sentence is:
Who needs dragons?
Which means 'Dragons aren't very useful', or:
Who needs a dragon?
Which means 'Why would anyone want to own a dragon (as a pet)?'
The reason it's "Who needs..." and not "Who need..." is because of how this verb conjugates:
"I/You/We/They need", and "He/She/Who needs".
It can be correct, if "dragons" is used as a name. You might be playing a card game that includes a "dragons" card: the ownership of such a card might confer magical strength, and the card could be referred to as "a Dragons".
"Who wants to trade a dragons for an invisibility?"
At the risk of being pedantic, there is a possibility by which it could be (almost) correct. If the phrase 'Who needs a dragons?' is only part of a longer sentence then maybe it's correct but just missing an apostrophe.
You could correctly construct for example:
"Who needs a dragon's heart?"
"a" or "an" basically means "one". "Dragons" is the plural of dragon — meaning more than one dragon — so you can't have "one dragons". This can be extended to other nouns (things). You can need "an apple" but not "an apples".
"Need" and "needs" are verbs (actions or states of being). Verbs must agree with their subjects — the things that are doing the action or being.
Singular:
He needs a dragon.
He needs dragons.
Notice how the verb is the same no matter how many dragons are being discussed, because the verb only cares about the singular "he".
Plural:
They need a dragon.
They need dragons.
In your example, "who" can refer to any number of people, so it is plural and uses "need".
Who needs a dragon?
Who needs dragons?