Ayuh,...... As noted above, there's supposed to be a stainless washer that sits on top of the shift spool, that holds the shift foot up into the shift shoe,.....
Ayuh,...... Donno what happened nor how,.....
As for welding it back together, tig, or mig might work, with it on the bench, not on the boat,....
'n, without pictures, I Guess it could be run, as is,.....
Nope,..... But I once used a Sierra bellows kit on my ole Alpha 1,.....
After 5 or 6 years, it didn't leak, but was Extremely bloated, so I changed it out for a Merc / Quicksilver kit, which is still on that transom assembly,....
Ayuh,....... That end doesn't need to be glued, the ring holds it in tightly,.....
To push the ring into place, spray the bellows with Quicksilver Power Tune 1st, 'n it'll slip in by hand,.....
Ayuh,...... There's a clip, inside the transom, that allows the fitting, 'n hose to move out enough to attach the hose, then push back in, then put the clip back on,.....
Before you start, read this thread about the pitfalls though,.....