1. に has a meaning akin to the english 'at'. For もらう, に works in a similar way to から, giving the idea that the gift came from that place. Therefore, it may mean that the flowers gave her courage and made her heart beat.
2. The っけ, according to rikai-kun (a chrome plugin that makes reading japanese a bit easier), it is a particle that indicates someone trying to remember some information. e.g, did those flowers give me courage...?
3. This sentence has the implication that the singer believes that 'there's a path there'. The japanese love to be ambiguous, because one can never be certain of something, so the word はず implies a very strong expectation that it will be true (and as far as I recall, this assumption is usually based on prior experience).
4. Throughout this song, the singer seems to be addressing herself, although possibly an audience as well. Anyways, in that sentence, she sings わたし. In others, I definitely get the vibe of her addressing other people.
5. Another option for this part is 'remember and don't forget'
6. そう 歩き出した その一歩が あ・・・
Not sure about this one, but 歩き出した seems to say something like 'set out (on a walk)'. A thing I've notice about the ます stem of verbs (end with い), is that they are usually verbs turned into nouns. Thus, this sentence seems more like 'That first step when you started walking', not necessarily in those words.
7. For this one, it seems that 描き出す can also mean to 'imagine'. (to pull out a drawing from the mind)