I wouldn't take this song, which looks a bit tongue in cheek, as a model of perfect English! I don't really think that sentence makes sense as it stands. You could take "hail" as an imperative verb, in which case there is no final "-s", but then the "to" doesn't work, because "hail" is a transitive verb that doesn't need a preposition. A more commonly found expression is "all hail", either on its own, or as a greeting ("All hail the king!"). It's rather archaic and only used in a jocular fashion now as a fixed expression. It's one of these expressions that got fossilized as its own word, like "goodbye" or something, but I think grammatically, "hail" would originally have been a noun rather than a verb, and "all" would have been an adjective. Also note the poem and now US presidential anthem "Hail to the chief", where "hail" again looks like a noun. (Note that if you use "hail" as an imperative verb, it would lose the "to": "Hail the chief!") Coming back to your song, I suspect that someone heard "All hail" and either deliberately or unwittingly reinterpreted "All" as a pronoun rather than an adjective, substituted "everyone" as a different pronoun with similar meaning but without the adjectival function. Then they had to use "hail" as a verb rather than as a noun, but then got confused with the "to", or they just threw in some random syllables to make the thing scan. Just a guess, and probably more analysis than it really deserves!

The verb is in the base form because it's an imperative, like 'Everybody come here!' or 'Everybody listen to this!'

Повелительное? Не подумал об этом... А порядок слов правильный? Разве при повелительном наклонении не должно было быть hail на первом месте? Hail everyboy..?

Повелительное наклонение.

Yes, 'hails' would be grammatically correct as 'everyone' is an indefinite pronoun and is singular. However, 'hail' in this context is still correct, as it is used here to create a sense of immediate urgency, a call in the present tense for people to call out (i.e. 'hail') the 'Pumpkin Song.' Examples: Everyone, hail your leaders! Hail their glories and achievements! (A politician might say this when speaking to a crowd) Everyone hail to the greatest sportsman of all time! (A sports announcer might say this) Hope this helped!