There will be other opinions. I'm a bit of a crude woodworker, but my engineering background forces me to do all kinds of crazy mental gymnastics when I splice something. For a rail that supports a thwart, I want my spliced piece to be quite long and I also want the angles to be very shallow. On one I did recently, I added a piece that was about 30 inches long to fix a break. My splices were about 4 inches long, each. The piece I spliced in was cut to match the shape of the original rail and then I formed it before I cut the tapers. I made a small form to bend the piece before I installed it. You can take a line off of the other rail to make your form, assuming it is true. Remember that whatever shape it dries to will probably spring back a bit. Take that into consideration when you make the form. Over-bend it. I suppose you could make the piece more simply with a table saw and a belt sander?
When I cut the tapers, I did the cut on the boat and cut the original and new piece at the same time. I used a hand saw to make the cuts. I left the splice a bit long (like about one tenth) and then massage it to fit before gluing it in place. I snuck a few small dowels in place from the outside to help hold the position while it cured. I used G-Flex, but I suppose a lot of people might use TB3 for that same repair. I like the G-Flex because of the strength of the bond, but also because it has such a slow cure time. If I decide to get fussy once all of my pieces and clamps are in place it allows me to fiddle.
The break near the deck is a bit easier repair. You can splice in a shorter piece there since the deck gets screwed in place. That will hold things together without all of the load on the rail that a thwart delivers. I would still use a nice long taper there.
For the seat, I would probably replace that board, but a splice would save the original wood, which is gorgeous!
My stretching set up is pretty hokey. Eyebolts, two by 4's, a come along. I may have some pictures.....Your question introduces an opportunity to discuss the other way that canvasing is done. There are a lot of folks doing the job on sawhorses, upside down. I haven't tried that....