Identification: Identification needed, gifted tree

Hello there!
I hope y'all doing good this days. I recently acquired this plant from a moving gig done in the city of New York. I had no time to ask what kind of plan it is or the kind of care it needs so I was wondering if you pros can help me out! It seems like it might need some extra care urgently... :( Take a look at the pictures and help me out if you can!
Thanks!

 

Welcome to the Forum!
Ficus lyrata....maybe?

Hope you are doing OK, too.

 

Plunge the pot in a tub filled with clean water until the soil stops bubbling.

 

I suppose, that the plant needs some light urgently.
Plants are living organisms, you can't place them away from the sunlight, unless if you replace it with a decent amount of artificial light from grow lights.

 

I agree it looks like Ficus lyrata. Those plants like consistently moist and warm conditions. They will never do well when placed at the front of a heater. You should move it immediately.
When watering pour the water slowly, the best way is to do it in very small amounts over a period of several minutes until the water starts showing in the outer container. After another few minutes discard excess water.
You should also move the plant to a bigger pot with fresh, good soil, but wait until it is in a better shape. Normally the best time for re-potting is spring, but here we are dealing with an emergency. When re-potting remove dead roots.
After the leaves are no longer wilted you could start feeding it, but very, very lightly. The soil in the pot looks entirely devoid of nutrients.