Hmmm, I'm not as familiar with vintage crochet tools. I feel like going with bulb stitch markers in plain metal colors might be okay, but I'm not 100% sure on how old that style of stitch marker is. Bulb stitch markers are a type of locking stitch marker that looks a little bit like a light bulb in its shape. I know some people will use things like safety pins for stitch markers, so if locking stitch markers aren't quite giving the right look and feel. I'd also recommend going with straight metal or wood crochet hooks over ergonomic ones. I don't know how common ergonomic handles or plastic hooks were in the 50s, but straight metal or wood handles were absolutely a thing then.
I figured that you probably wouldn't be going too depth into different stitches, which is why I focused more on tools and such. To answer your specific questions:
I'm not thinking of a specific term for mending crochet work. I know darning is used for repairing knit and some fabrics, and it can be used for certain types of crochet repair. Darning would be done with a needle and is often used for fixing holes. For larger fixes, you could use a patch, which in this case would be crocheting a separate piece and attaching it to the spot that needs fixing, or undoing around the damaged section and crocheting it again.
Crab stitches, sometimes called reverse single crochets, can be used as the final row to help strengthen the edge of a material. They also adds a different texture to the edge.
Frogging is the term used for undoing/unraveling stitches. The term came about because you are 'ripping out' the stitches, which sounds close to 'ribbit', which is the sound a frog makes.
I'm not sure if it's really unique, ribbed stitches could be a fun addition. It creates a stretchy fabric that is often used for hat brims, sleeve cuffs, and other places you want to snug fit with some stretch.
And, yeah, taking some creative liberties are to be expected when making a game like this. There is a fair bit of overlap between the knitting and crocheting world, and it would honestly feel weirder if you didn't include any knitting references at all.