Attach some kind of radial arm to the base of the pipe that is long enough to clear the concrete base. Unistrut and several hose clamps will suffice. Pound a spike into the ground at the end of the radial arm. How much good that will do against the force of the oak tree branches hitting the panel antenna is dubious. Having the pipe twist when the oak branches hit the antenna probably saved your antenna from destruction (as seems evident by the antenna tilt). If the pipe were secured in place, I'm fairly sure that the sheet metal mounting contrivance on the back of the panel antenna would now be twisted into a pretzel.
Incidentally, I would NOT pound a wooden wedge into the base bushing as it's like to split or deform the bushing.
Trim the trees.
Nope. It's fine (but ugly). The loss caused by polarization mismatch is fairly minor until you approach 90 degrees. Polarization Mismatch Loss in dB = 20 log (cos angle) For a 15 degree tilt, that's only 0.3dB. Even 45 degrees will only cause a 3dB drop.
Ummm... is that the Home Despot CAT5 on the ground? What happened to the waterproof direct burial CAT5? It will probably last through the winter, but all it takes is for you to walk on the cable, or some critter to chew on it, and water will get in. After that, it's just a matter of time before the copper corrodes into an intermittent.