Don't be concerned about the wiring diagrams in the Honda manual. They're not important here. I think Gadge was trying to point out that there are three different alternator setups available. From the pics you posted it looks like there is only one green wire into the rectifier cube and one red wire out so you have the little 1A charge system. This is just background information.
Yep; what I was getting at was that the number of charge wires, and their colours, can tell us which of the 3 this engine has. The 1A charge system is the simplest of them.
Good news that the Honda solenoid still functions. As Gadge says the can protects the internals from muck and moisture. You will need to carefully re secure the top to it. Carefully reposition the rubber seal that is pinched in the photo and try to clip the top back down. It may just click back. If not you'll need to try and secure it with a tyrap or two and depending on the condition of the rubber seal once it's repositioned a nice thin bead of silicon may be the go too. The key here is that the top needs to be secured to the can and that the inside is protected from water a dirt.
For sure. It will be a lot easier to do this if you take the solenoid off the engine first, I reckon.
Mark's pic of the new solenoid clearly shows how the 'retainer clips' on the can are punched inwards, to secure it to the top.
If the top wiggles fully back into place OK, punching these in again should work to secure it.