how can I fix these issues with 2D tilemap/blueprint movements?

To be fair, you’re going from 0 - 60, blueprint wise. But I will answer as best I can.

To make it go back and forth OR up and down, do

Because the TL is also a component, you can change it’s speed like

A sprite is definitely possible

PS: You can also make the sprite a parameter, and deal with these sprites with the pivot point in a strange place, using the construction script. Just come back if you need help on that.