When writing a verse for a song a lot of times I find it easier to sing if I leave out function words (demonstratives/conjunctions). Is this a bad habit? It seems to cause lack of clarity but I see it done a lot in poetry. I also get tired of using the word 'and' so often.
Example:
When I went outside my home I had a feeling,
something wasn't right. (that)
I guess I didn't have the time (but)
that is how I almost died (and)
I would just change to periods, especially for eliminating "and". It almost always works fine. It works in all your conjunctive cases:
When I went outside my home I had a feeling.
Something wasn't right.
I guess I didn't have the time.
That is how I almost died.
It might be a bad habit. It is not a bad practice. Don't do it if the meaning is damaged.
If the word is not necessary to the meaning, then brevity beats wordiness.
When writing in general, you can omit words by punctuation:
When I went outside my home I had a feeling: something wasn't right. I
guess I didn't have the time... that is how I almost died.
From an "acceptability" & literary point of view, this is perfectly fine, because it gives you a (more) unique voice. Given that it's a song you're writing, it's really not a problem, unless this is not the type of voice you want to project.