I think I know what kind of puzzle this is:
a reverse hangman puzzle, which has been popular on this site, and is of course even more popular as a traditional unreversed hangman puzzle.
Let it be, it'll warm you inside
Let it see, it'll warm you outside
We start off with a word or collection of letters (the solution), to which we can either add B to get something that warms you inside, or add C to get something that warms you outside. The words I can think of here are BLOOD, COAT, and CLOAK, but unfortunately clood and bloak aren't words and I can't see how a boat "warm[s] you inside".
Make it pink, it'll wake you gently
Make it red, it'll wake you harshly
I'm actually unsure of how these lines are supposed to work. Do we add the letters P-I-N-K and R-E-D to our word, perhaps with some rearrangement? Do we just add P and R? Do we somehow make the word more "pink" or "red"?
Give it freedom, and it's something you wear
Give it knowledge, it's an injury you can't bear
Again, not sure about this. "Freedom" could refer to spaces between letters (turning one word into two?), but "knowledge"?
Throw it in the flames, it's a sky reunion
Put it in the stars, it's a nice provision
Maybe we need to add something like B-U-R-N-T or A-L-O-F-T to our word?