Well, here is the deal, the log rolling over on and bending the cylinder was kind of a freak accident thing, You know now not to do that. And besides a
grapple is the proper tool to be picking up logs with. Yeah, I know, you don't have one, but you could have nearly bought one for the price of that cylinder replacement.
As for the back dragging of brush, you now know you got to be really careful doing that, you can get away with it USUALLY, but sometimes if you roll the bucket down too much and you make the bucket so that it won't slip over an immovable object then you know that a bent cylinder ram or even both of them is a possibility. Don't do that no more.
You can use the float position on your joystick allow the bucket to float over the terrain with just the weight of the bucket and the loader arms as the down force. This allows the bucket to float up over something immovable if you hit it. If you don't understand about float, ask some more questions.
As for back-dragging over even small trees, that is never going to have a good outcome. Tractors are amazingly tough, BUT there are some just "silly" things you can do to tear them up. Now you have been there/done that, so don't do that no more.