I'm just going to input my experience. Anyone with more experience can come in any time and refute what I am about to say...
From my research, ghost shrimp are extremely sensitive to water parameters and were typically bred not to last long- more bred as food for other species. I don't know how true this is since they're so hard to see! lol I bought 3 ghost shrimp last year sometime and they all died overnight. I know, in hindsight, it was my water and everything was new and not cycled or anything. But I vowed to never again own shrimp (because the spikes in water params overnight ended up killing my VT Lakitu).
So, I would ONLY add ghost shrimp to carefully monitered water.
Now, I will answer your questions but with my experience with red cherry shrimp (another dwarf shrimp but which were bred to be more hardy because they were bred to be pets and to withstand a wider scale of water params):
1. Do ghost shrimp eat diatoms? I found some darkish mass in her digestive tract and that's either my driftwood, diatoms, or my still dying bacopa. Shrimp scavenge for anything. I have seen mine sift through their poop looking for food. Diatoms are just decomposing waste/plant matter right?? If so, I have seen mine going through it
2. If so, can I rely on them to get their plant nutrition from the dead leaves/algae in my tank or should I supplement with wafers/fresh veggies for maximum shrimp happiness? Which veggies would you recommend? (I already supplement her with my omega pellets for animal protein) In my shrimp-only tank I supplement with algae wafers, they LOVE it!! They fight over it and just kick it all over the place. I have 11-12 RCS and they all do fine on like 1/4 of an algae wafer once or twice a week. They poop a lot so they don't need too much supplement food. I watched my shrimp eat the stuff off the roots of floating salvinia and marimo moss. They love picking through live plants and this is generally a fine diet. Some people I read about while researching getting shrimp said they don't even feed their shrimp in a live planted tank. And I just moved 2 adult RCS into my betta tank, I have NO intentions of giving them algae wafers bc I have an abundance of algae- their favorite food. Plus my bettas would eat the algae wafer.
3. Do they eat detritus worms? No. I had my shrimp eating frozen bloodworms but they don't hunt to the best of my knowledge. They prefer to graze on stuff laying around.
4. What about baby pond snails/snail eggs? Shrimp wwon't bother snails or eggs that I know of.
5. The girl I got has been clinging to her eggs for four days now. Is she going to eat those eventually? Your shrimp? They keep their eggs on their underbellies for like a month, in which time the eggs grow and mature. When they hatch, mom kicks them into the water randomly. She keeps the eggs on her for a day or so afterwards I think. Baby shrimp will eat the infusoria in live plants like its going out of style.
6. I want to get two more shrimpies. Is there a recommended gender ratio like guppies? Not that I want to breed them or anything, I just don't want two males hounding down my female constantly. I have 11 or 12 RCS of random gender in my tank, as long as parameters are stable and they have plenty of food they will just breed on their own. You can see fertilized females by the "saddle" on their backs. This means they have already been fertilized.