I will start out by saying I am totally clueless when it comes to plants. I have looked at the FAQ and searched other posts but I'm not sure if I can pin point the issue and would like someone to take a look at the pictures. As you can see, it look like half of the tree is dying and half is doing fine.
We are in a rental and when we moved in the landlord said to just water the tree weekly.
The little grass patch under the tree you see is fake grass. So in order to water, we have to find little openings and shove the hose in there. I'd say we let it run for about 10min at a time. My husband does it most of the time so I'm not positive on that.
From what I can tell the soil does not look likes it's dried out or overly soaked... But I can only lift up a little edge of the fake grass in order to tell. We've also never fertilized it, only watered as we were instructed. We love this tree and want to save it.
You can also see one of the branches looks like it's rotting. If you look at the tree head on in the first picture, the branch that is rotting(?) is the one on the farthest left.

Any advice would be much appreciated! Thank you in advance.
Rene