"we make our own sense" could be what Susanne suggests, but another interpretation is that it is about the concept that humans are "meaning makers" that is, we look for meaning in our lives and existence, and that this meaning is different for everyone and that we make our own unique sense of this world, this existence. It's not common and therefore open for interpretation - I suspect the context you found the phrase in would help explain it.

I'm taking my time on my ride. - I have not heard this one, but I would guess that it means I am not in a hurry. It could be literal and mean I am not going to hurry down the highway on the way to my destination. It could be figurative because we sometimes say that life experiences are a ride. So, I am taking my time, enjoying, and savoring the ride/journey/time. We make our own sense. - I have not heard the song Scott mentioned, but I think this is something said between close friends who know each other well and have lots of private jokes. We make sense to each other even if no one else understands.

1." You can count on me" means they can rely or depend on you. For example, your friend asks if you will help her move house on Saturday. You tell her you'll be there, she can count on you. 2&3. I do not know these as expressions. I have seen 3 in a song, but I wouldn't use it unless I thought the person I was talking to knew the song.