Bad strut rod bushings?

Well, your bushings need replacing for sure, although I'm inclined to agree with Dana67Dart that bad bushings probably are not the reason it pulls hard to the right when applying brakes. Grease on the brake lining on that side can make it grab. Other possibilities are brake lines that are rotted internally, one side more than the other. Or even a tire that has a tread that's about to fail and separate from the rest of the tire.

Edit: OK, now you are saying it pulls to the right on acceleration, too. That is not likely a brake issue, unless one side is failing to release fully for some reason.

If it were my car, I'd fix the LCA and strut rod bushings and then see where we are.