Had a look at the project.
I suggest you round the edges over first. For this you need a round over bit (similar profile to what came with the router), carbide-tipped, with a bearing instead of the integral pilot of your old bit. An offset base would be nice, but you can get by by just having a scrap piece of the same thickness as the plywood, to stop the router tipping - it happens.
1. Although you can do the notches with a router (but then use a straight bit with a half-inch shank), understand that you will be pulverizing the 3/4 X 3/4 pieces of plywood to be removed. Fairly tedious, even with a powerful router, not to mention dusty.
I would recommend that you get rid of most of the waste with circular saw and jigsaw - precision not required, better to leave a bit of waste. Then do the final cut to the line with the router. For this purpose, any old fence will do - a straight piece of wood, with a half-hole to accommodate the router bit (actually, if you pivot end end of the fence, you can slowly swing it across, and let the bit cut its own housing). The only thing about the fence, it should be higher than the thickness of the plywood, so that the top of the bit is proud of the plywood. For safety, glue/screw/nail something over the bit cavity - if you are not used to this type of tool, you do not want to even possibly get your fingers near the spinning bit.
2. Do all the saw cutting first, then set the fence with some test cuts on a piece of scrap. The backset of the fence is the same for all the notches, so once clamped down tight, you can do all the routing in one shot.
3. Just a thought - if you use a 1/2” bit, the bit will actually stand out from the fence, so the hole in the fence is not even required, as you will be shaving at 3/4” from the front of the fence.
4. For the above operation, neither template, bearing or bushing is required. You will have to finish the corners of the cuts by hand, as you said.
5. For the dados, you will have to have the router out of the table, handheld, ready to plunge. The easiest would be to use a plunging pattern bit (I.e the ends of the blades also cut - some straight bits are labeled plunge bits, but actually do not bore into wood - they cut from the side). Like Charles said. The bearing should be on the shank side of the bit. Make a template of your dado by cutting the rectangle by hand in a piece of thin plywood or hardboard. The size of the board should be at least three-quarters of the diameter of the router base, measured from all edges of the dado cutout. With experience it is possible to use a smaller board, but you do not want to mess things up while trying at this stage. Set the depth of cut (remember the missing piece, you will need something here to limit the plunge depth) such that the final pass goes right through the plywood (at least, that is what I understood from the plans). Either place the board on some type of sawhorses, or have a sacrificial piece of scrap wood underneath, otherwise you will dado your workbench.
6. For this purpose, you do not want a long bit: if it is too long, the bearing will not bear against the template on the first pass, and you will chew up the template. If it is not long enough, less of a problem - once the bearing is below the template, it will be bearing against the previously routed edge - as good as the template.
7. You might want to take the rounder-over bit mentioned above, and take a pass around the inside of the dado cut - nice rounded finish, easy on the hands. The direction of feed is important - read the material referenced by Stick in your earlier post. It also shows how to set depth of cut, for various profiles of bit.