You are correct that the bottom corners of the sails will be secured after going into the bottle. This is the way I've always done it and your right the yards can't rotate otherwise. The hard part in securing the sails sometimes one side sits to high and another to low. I suggest adding the lifts as you see in Alans diagram above. I use thread blocks so theres no hole drilled. Tie a thread block just above the mast and secure the line from one end of the yard through the black and on to the other. The line will slide through the block and still allow the yards to rotate. Once its in the bottle you can rotate the yards in there proper position and put a bit of glue on the thread block. This will help keep them in the right position. Gluing the lines at the bottom of the sails will also help keep them in the right position. Using both will secure it all together.
I'm a little confused with the second section. I'm hopeful Alans illustration is helpful. I think you have a great set up so far. THis is what it looks like and tell me if I'm not understanding this right. You will be inserting the hull first and then the masts separate from the hull. The mast will be inserted into the hull and then the back stays, glued to the side of the hull. From there you need to secure the fore stays. I think Alans diagram shows this how this works really well. The only minor drawback is it shows a clipper and not a galleon. The principles are the same but its hard to compare as the clipper has a lot of masts and doesn't have the cross trees. I found it hard to find a non convoluted rigging plan but here's something.
First some terminology and you may already know this. The cross trees are the parts where the sections of the mast come together. The Forestays on the real ship are connected at the cross trees. You can see above how the forestay runs from either the top of the mast to the cross tree one section down on the mast in front of it, or from a cross tree to the cross tree on the next section down. They aren't necessarily parallel but they look like they are. On a rela ship they are secured and each are separate lines. For a ship in bottle your simulating this but they are one continuous line. For instance one line from the main mast gallant crosstree that connects to the royal section, run to the the fore mast top and then to the bow sprit the line can then be run out of the bottle and tightened up and glued down once the ship is inserted.
Which is all an over explanation of run the forestays between the cross trees and out the bottle. I hope this is helpful. Let us know if you have more questions.