What should be done about this concrete retaining wall?
You have several issues: 1) Diagonal cracks, 2) Deadman movement, 3) Tree root stress, 4) Fence movement, 5) Water buildup behind wall. 

1) Diagonal cracks are an indication of wall stress load failure. That is to say, the wall is failing because of an excessive load on the wall and a lack of reinforcement in the concrete wall to resist the load. (Vertical cracks are an indication of temperature or expansion failure...which is much easier to fix.)

2) Most alarming is the fact that the steel plates with the steel rod and bolt is called a deadman and it’s failing too. Evidently a deadman was installed in at least two locations (that I can see) to help hold the top of the wall from tipping over. If you look close, you can see a gap (space) between the steel plate and the concrete wall. This is an indication that the deadman has failed. Perhaps the rod has come loose from the deadman. The deadman is doing nothing. 

3) Yes, probably most of the “load” on the wall is from the tree.  Of course as the tree grows it spreads out and “pushes” on the wall. However, as the tree sways from the wind, the tree roots “push” on the wall too. The tree needs to go...

4) Any movement from the fence will add stress to the wall too...similar to the tree in Item 3) , above.

5) water is heavy and puts tremendous stress on a wall if it’s not collected and drained away...especially in a climate like where you live. When you have many inches of rain in a short period time the subterranean water doesn’t have a chance to dissipate. When it builds up against the wall, that’s a lot of stress. 

I don’t know of a way to save the wall. It will continue moving until it falls. You could slow the failure by removing and killing the tree. However, be careful when the tree falls, it could put a huge thrust on the wall. 

BTW, I wish I had a Bronco to go 4-wheeling...