Yes, there is a noticable crack in the foundation wall that lines up nicely with the end of the crack in the basement floor. I've considered the issues of the foundation sinking more and of needing serious support for the jacks. The best plan I have so far is to jackhammer a 1'x1'hole in the floor at the "sunken" corner, and use a post hole digger to dig down as far as I can, then make a concrete w/rebar post that is topped with the 1' square new concrete pad (tied to the floor) to set the jack on. Will make the pad 8" thick. Hopefully this will support the jack with no problem, and stabilize the foundation in that corner.
Re supporting the joints, the house has standard rim joists that can be seen from the basement (no insulation!), so I can get a beam all the way out to the joist that runs parallel to the floor joists, and tie the beam to that rim joist then run it under and perpendicular to the floor joists, along the rim joist. It will run along the basement wall to be supported on the other end with a post on the un-sunk part of the basement floor, with cribbing underneath.
Re the "what if it falls", I plan on jacking very slowly over several months, supporting the rims every 1/2" or so.