The automatic trunk opener does not open trunk the whole way. It also may not close truck. If I try to close manual i get resistance but can close it. Some times it works ok.

I would guess it's a weak hydraulic strut. It's on the right side of the trunk frame. There are also non-powered "Lift-o-mat" struts on either side to aid in carrying the weight. If they are bad, it can make the trunk open more slowly or be hard to open.

What is making the hydraulic strut weak? Low Hydraulic pressure, leakage, pressure loss, etc? Will replacing the strut solve the problem?

When I try to close the half open trunk lid, it pushes back? I can close and latch it. It works some of the time but sometimes it just opens half way.

The seals in the cylinders with age and usage. A weak inner seal can make the cylinder slow and inefficient as fluid inside is able to bypass it. There are also outer seals that will cause fluid to leak out of the cylinder.

When the lid stops raising, is the hydraulic pump still running? If so, then it sounds like the cylinder is trying to do it's job but is too weak. This could be from weak inner seals, but like I mentioned, it could be that the "helper" non-hydraulic struts are weak and not giving it enough assistance. When you say it's hard to close, had you ever closed it manually? It does take a bit of effort, but not more than you could give with one hand - you just have to keep pushing it down as there is constant resistance.