"corretemi IL MIO ESSERCITO per favore... T.T"

-The title is not correct, I think you actually wanted to say "Correggetemi l'esercizio per favore", but anyway you should rather write something like "Potreste correggermi questo esercizio perfavore?" meaning "Could you please correct this exercise for me please?", it is more polite. Plus, you don't have to specify again that is your exercise with "mio", because you wrote "correggetemi". The "-mi" at the end of the verb means "a me=to me" therefore it already expresses a certain degree of possession.

-correggetemi: from the verb "correggere" to correct. Verbs in Italian are pretty though. In English you would say "correct me", however, in Italian we attach the pronoun at the end of the verb, so that it would be: "correggete (present tense, second person plural) + mi (me)= correggetemi".

-The sentence is grammatically correct, but in conversation you wouldn't say it that way, you would rather say:

-Sta proprio per arrivare la stagione perfetta per uno Spritz, o anche due!