could it be a Heart-Leaf Philodendron?

Looks like plain old Pothos to me, aka Epipremnum.

Sorry, I missed the 2nd question, the younger shorter ones don't neeed to 'catch up' but if you trim the longer parts & place them back into the pot it will help keep it full & lush looking.

You COULD also root those cuttings in water for a new plant altogether.

Thanks!
When you say "trim the longer parts & place them back into the pot it", would you mind giving me a little more detail so I know I do it correctly?

Same for rooting them actually. Do I just cut them anywhere, and put it in water for a few days until I see roots?

Sorry, I see my ID is not quite right, I'll let someone else do it, I don't know the exact name of that plant it's not quite what I suggested, but LIKE that.

Yeah, pretty much cut them anywhere, like a 6 or 8" piece & pop into water 'til you see roots.

Yep, you have a Heart-Shape Philodendron,..Philodendron scandens.
Cut back where the bottom stems are getting a little spindly. Root, then plant in the same pot with mom. It'll look a lot fuller.
Although Philo scandens don't need direct sun, it wouldn't hurt to give it a little more light. Artificial will do. Notice the leaves on the bottom aren't as large as the upper leaves?
Your Philo needs more light and/or humidity.

It's a very nice-looking Philo. Toni

Like most philos....if you train them to grow up-right, the leaves will get progressively larger.