The difference between 色々と手続きがある/色々な・・・ is only grammatical (色々と[adv.] modifying ある / 色々な[ adj.] modifying 手続き), and I don't see any difference in meaning.
色々と手続きがある can be 'translated' as There are procedures variously, which obviously is not a normal sentence, but I guess many English speakers would understand it as There are various procedures if forced ...
In the most straightforward interpretation, いつも modifies the whole of 音楽を聴きながら勉強します, in which the adverbial clause 音楽を聴きながら modifies the main verb 勉強します.
This is because いつも is an adverb of frequency, and this kind of adverb tends to work on the whole sentence. Thus, the sentence is talking about the frequency of your habit, and your habit in this case is to ...
This is indeed an uncommon adverbial usage of 勢い, but it means something different from what you are thinking:
4. naturally; necessarily
So what is the previous sentence? Does "naturally" make sense?
"Hit with force" would have been 勢いよく打ち付けた, 勢いをつけて打ち付けた, etc.