Sheila,
Welcome to the Grumble! I hope you find our ideas as interesting as many that I see on the framing forum on your side of the pond.
Regarding gallery wrapped canvasses, over here they are usually done on heavier strainer bars up to 1 1/2" square and either the image is wrapped around the outside face of the bars or, in some cases, a black margin is printed/painted to the outside of the image which covers the outside face of the strainer bars. Most of them have a brace down the middle of the long sides to strengthen them.
I recently built my first gallery wrap frame from scratch and sort of learned as I went. You should relieve (bevel, much like most stretcher bars are bevelled) the face of the strainer bar, that which is behind the image of the canvas before you chop and join the strainer. Also, the brace should be slightly narrower than the thickness of the strainer so it doesn't leave its outline down the center of the canvas after all is completed. When attaching it, you would flush it up to the back edges of the strainer which would leave it inboard of the canvas.
I rounded the edges of the strainer that were in contact with the canvas with a hand plane. You could also run the stock through a router or sand the edges to soften them.
Regarding the canvas corners, on most of our bought gallery wraps, the corners are folded square with the corner of the strainer on the bottom and top and stapled in place. That leaves the sides of the stretched canvas clean and with no folds which is preferable if one is to hang the canvas by itself. I didn't have any trouble with the folds lying flat, you simply have to take your time and be careful when you fold so the canvas is seated deep in the under fold. I did learn that it is easier to make that corner fold before you staple too close to the corners. I was about 8" from the corners and I will probably leave more room, 12" or more next time. I got the corners folded OK but it would have been easier if I had a bit more room.
Good luck.
Framerguy