1.the word "past" in this sentence is "adj" or "adv" or "verb"?? which word does it modify??
In this sentence, past is functioning as a preposition (of time)
dictionary.com
prep.
Beyond in time; later than or after: past midnight; a quarter past two.
Beyond in position; farther than: The house is a mile past the first stoplight. They walked past the memorial in silence.
Beyond the power, scope, extent, or influence of: The problem is past the point of resolution.
Beyond in development or appropriateness: The child is past drinking from a bottle. You're past sucking your thumb, so don't do it.
Beyond the number or amount of: The child couldn't count past 20.
2.I'm not good at English. I always thought that the sentence means "the older guys are going to be too old to party". I don't understand, what is the key word that make us know that the sentence means "they are too old for this type of behavior".
"They are way past their prime" simply means that their "prime", their ideal age for this type of activities, is in the past. So they are already too old for this type of activities.
3.If the sentence "these older guys, still partying way past their prime" means "these older guys, who are still partying, are way past their prime"why don't it has the word "are"??
The only reason I can think of for that one is an informal use. Any other suggestions?