If the forks were checked out by a mechanic, there should be no need to loosen anything to straighten the triples/forks, as the forks should have already been removed and reinstalled.
Assuming that the forks indeed were not checked properly, take the forks off and check the runout of both fork legs. Any more than 0.2mm and the forks are trash. Also check the triple trees on a flat surface, like a piece of glass. If they're only slightly bent if any at all, you should be able to straighten them. If they're bent by a good portion, trash them.
No, you cannot reweld the nut back on to the swingarm with just a torch. $200 is a bit high, but that is a fair price for welding aluminum, especially thin walled aluminum. The reason why the price would be so much is that to the welder, it's an unknown aluminum alloy. Can't just grab some welding rod and weld up on an unknown alloy.