I would be on the "perfectly okay" side of this argument – given that it's a song lyric.
Song lyrics often bend grammatical conventions. They often stray from strict semantic rules and are frequently more concerned with meter and rhyme than normal conversational patterns.
I'm incessantly reminded of this during December, when I hear lyrics such as:
O Christmas tree, o Christmas tree
Such pleasure do you bring me 1
Late in time behold Him come 2
I don't talk like that. If I was going to bedeck admiration on a Christmas tree, I'd structure my sentence more like this:
O Christmas tree, you bring me such joy!
and if I wanted to remark about how someone finally arrived after a very long wait, I'd say:
Wow! He sure was late. It's about time!
So, back to your friend's lyric:
I'm the best from all the crowd
I've never heard anything like this. It usually goes like "among the crowd" or "in the crowd".
Sure, it's a little clunky, especially for something so self-aggrandizing, but I can still get the gist of it. There are a lot of people out there, and your friend stands out as the best. As for whether from would the best preposition, I'd agree that among might be a better fit – but that word's extra syllable messes up the iamb.
See me deeper and scream loud
Shouldn't this be "scream loudly"?
Juhasz's answer sums this up perfectly: Native English speakers regularly use adjectives instead of adverbs. This is definitely common in song lyrics.
The one other point I'd like to add is that loudly hardly rhymes with crowd. If your friend was writing an essay for a college application, your recommended change would be a good one. But, in this case, it ruins the rhyme, so I'd recommend leaving it as-is.
Catch good vibes and inspiration
Feel the power and my relation
What on earth could "my relation" be? A relation of mine is something which is related to me, but that's absurd, since it's obviously unnatural.
A little mystery embedded in the song lyric! This isn't the first time and it won't be the last. I'd probably assume that, by "feel .. my relation," the lyricist means "feel my connection with you." But if you think those lines are obtuse, try Wooly Bully, American Pie, or Octopus's Garden. Not all songs make perfect sense.
I think a disconnect happened when the native speaker you mention in your question evaluated the four lines as a song lyric, while you dissected them looking for impeccable English. Well, four-line quatrains are not the place to look for impeccable English! If faultless English is what you're looking for, try the editorial page instead of the record jacket; you'll have better luck there.