Yeah, I did my whole bucket in Sintra, it can be a pretty hard material to work with sometimes, but it does make for a really nice strong and smooth sculpture. You can check out my thread here if you want, though my initial assembly part is the least documented unfortunately.
What I'm seein from your pics it looks like you might have gotten too ahead of yourself in some places. You pretty much don't want to cut out the T-visor or remove the internal support skeleton until everything is already curved and stably in place, as otherwise it can cause all sorts of problems with the structure and curvature of outer-layers. The outer layers are pretty much just two big rectangles that you curve around into circles, if a big section is missing in em it can make getting an even consistent curve a nightmare.
Something that really helps is to pre-form the pieces too a little via heat-curving. Just bending them straight-up can create a lot of stress on the plastic which is where I suspect might be where those cracks came from. Heating the plastic up and curving it around a large bucket or something puts the plastic into a natural curved shape that's much easier to work with. Careful to keep the heat even through the piece though and not overheat and specific part, as it will make that part more bendy than the rest and can create a inconstant curve there too. Also Sintra is PVC, which releases dangerous gases when heated, so have very good airflow and wear a respirator if you can.
As for bonding agent, I found cyanoacrylate superglue to be the best, it bonds extremely fast and the thin stuff will seep some down into the cracks you're trying to bond. You can pretty much do spot welds with it while curving your forms together, tacking up one section before moving to the rest. Much better than slower curing stuff like plastic cement.
As for the dome and supplement pieces, dunno. You'll pretty much have to hope you can find some ball shaped thing somewhere that's the exact diameter you need. It's going to be a pretty tough build though if you don't want to use any bondo, it's pretty essential for smoothing things up and hiding seams. If you're just worried about the fumes, you could use something like Apoxie Sculpt instead which is non-toxic. It's more expensive and difficult to sand though.
