First, I would validate, that without seeing the project, plans and work first hand, all I can legitimately offer is speculative at best about your specific case.
As for some of your questions:
1.)---Would it be safe to have one full-sized peg and one slightly smaller in diameter, holding the post and beam together?
Personally, I wouldn't accept this in a joint union employing Pegged union. The Peg in question would be driven out, and a bespoke Peg created to fit more snuggly.
This then raises the issue of losing the Draw Boring effect that this type of joinery is usually supposed to incompass as part of the union within the joinery system matrix. Since the frame in this area of your project appears to be up already, and I will infer you are satisfied with how tight the joinery union is presenting. As such, it...should be (??)...acceptable just to get a better fitted bespoke Peg to satisfy the future loading this component will take; understanding that the augment Peg is not overtly enlarged in the fitting process.
2.) When making pegs by hand, with a shave horse, what size do you try to get? Slightly larger than the peg hole, or can it be somewhat the same size?
This...feel for it...comes with experience when creating and sizing Pegs/Trunnel. Keeping a Go-No Go Gauge close at hand will aid in getting the feel for what size is best for your needs. In general the Peg is oversized according to the species it is made of, and the species of wood it shall be driven in.
3.) Also, which shape do you try to get? Round, square, octagon, etc?
Now we can speak further to sizing, as I tend to only use octagonal or square Peg/Trunnel in my work...If I employ them at all, since most of my designs are gravity joint or Draw Wedged unions.
With the octagon shape (which I find the best and most often historically correct format in general)you can fashion the facets of the octagon to be exactly the size of the hole...no larger or smaller. Then, the terminus of the facets will...bit into...the work when driven home and usually crush the surrounding grain just enough to effectively merge in grain pattern to both a pleasing aesthetic and functional snugness.
I would not here, that I do tend to Rive out my Peg rough stock yet turn to a Table Saw to dial in the exact size rapidly. If historic work the...exact sizing...is completed on a shaving horse, or Planning Bench with large Jointer Plane, and sizing jig.
This then takes the conversation into the amount of Taper to place on the Peg/Trunnel? This is subjective to the individual Timberwrights work/project, and/or regional historic variants that need (or should be) replicated if doing restoration/conservation work. There are a number of other conversation here on the forum worth reading that covers this subject and I would strongly recommend researching those and reading them to acquire a deeper understanding of this topic.