みてー is a contracted form of みたい ("is like ～"). It's an instance of /ai/-to-/ee/ contraction. 上げて is the te-form of 上げる, and 落とす is a verb. Therefore a very literal translation is "It's like I raised it and then dropped it".
上げて落とす is a slangy expression which may be called an idiom. It roughly means "to set someone's expectations and then disappoint them", "...
This 小せえもん ("trivial things") is a paraphrase of 国のため(とか). It's read like trivial things such as "for our country" or "For our country"... such trivial things. In other words, this guy is making light of petty nationalism, and seeing something even bigger than Cuba.
EDIT: In case you missed it, this が after 凡人共 is a derogatory vocative-like particle, e.g., "...
The canonical rule is as follows:
Use hiragana for a subsidiary verb following a te-form, e.g., (持って)いく, (読んで)みる, (作って)おく
Use kanji for the second component of a compound verb, following a 連用形, e.g., (やり)直す, (食べ)切る, (降り)始める, (読み)終わる, (動き)回る
(Except for verbs that are usually written in kana anyway, e.g., (言い)かける, (考え)あぐねる)
Therefore, ふりだした is normally ...
たくて is the te-form of たい "want to". The form たくて only has one function, to make a subordinate clause of the verb before ("wanting to V", "want to V, so/and"), that connects to a main verb (predicate), unless it is used with certain idioms that need te-form for other reasons.
Then where did the main verb go? In this case, the sentence is inverted. The ...
This 叩き込め is nothing but an imperative (i.e., "Crusaders, throw your fist!"). Although 叩き込め is the only imperative verb in the entire lyrics, it's used four times, so you can think it's the main "message" of the song.
First, 頃 right after another noun is always read ごろ due to the rules of rendaku. It can be safely written both in hiragana and in kanji, but my personal preference is kanji.
Next, the basic meaning of 頃 is closer to "days" or "season" rather than "time", as in 学生の頃 ("in my school days"). It almost never refers to a short period of time within a day. It's ...
The やる here can mean "to kill" or "to beat up", depending on context.
See: What does やっちまえ mean?
やられる is its passive form, "to be killed/beaten up".
やられて(い)る here means "to have been killed/beaten up".
This is Possessor's Passive structure (持ち主の受身), a kind of Indirect Passive structure (間接受身構文). E.g.
（私が）泥棒に財布を盗まれた。 ← Possessor's ...
'To vape' is 電子タバコを吸う
The noun 電子タバコ literally means electronic cigarette and the verb 吸う has many meanings aside (not just smoking), it can also mean to inhale, breathe, suck etc.
This Japanese game (はぁって言うゲーム) has a card that shows how versatile the 吸う verb is (funnily enough, none of which involve smoking).
Dropping of い is a very common colloquialism. It is heard in all sorts of informal situations, and kids probably learn how to say 降ってる before 降っている. You should use the long version in formal settings. There are similar contraction patterns, and てる and ちゃう are especially common among them.
I basically agree with the other answer. But, we need to connect them with the boxing a bit.
I adopt the definition もったいぶらない ; doing something without hesitation/reluctance and apply it to the boxer.
So, probably the boxer prefer to fight against his opponent very aggressively without considering stamina i.e. no hesitation.
According to the wikipedia, I ...