The 'saw thing' is the escapement rack, which meshes with the toothed escapement wheel.  When you raised it up, it came out of mesh with the wheel and that is why the carriage would not 'catch' and stay in one position.  When you took the carriage off, you disturbed the ball bearings and their carriers.  The little square headed bolt is the final stop that prevents the carriage coming off its rails. Unfortunately, you will need to go to a professional, or at least a talented amateur repairer, who knows what they are doing.  It would be nearly impossible to describe exactly how to put the carriage back on properly in a few words.  I think that is why everyone is sitting on their hands and not replying to you.  They are thinking, 'How can I even begin to reply to this ?' 

Hi Allmc

​typewriterman pretty well said it, you need serious help on this one. What I can tell you is the long plastic things are the ball retainers and the little stars in the middle of each retainer is called the anti-creep wheel and keeps the balls correctly timed with the carriage in its rails. The ball carriers have to be correctly aligned and timed as the carriage is being reinstalled, they're tricky little devils to put it mildly. It took me several attempts to get the carriage back on and correctly timed on an Olympia Splendid 33.

The only machine I found more tricky was the Olivetti Lettera 32 with its 4 separate balls and anti-creep wheels, I simply didn't have enough fingers to hold everything in place at the same time. Hope this points you in the right direction. All the best,

Sky