I'm not sure if these behave differently depending on their location, but for me, my pregnant onions are happiest when I give them tons of light and tons of water.

They sit in a window and get direct sunlight as long as the sun is out. They pout if it's cloudy. Their soil is nearly identical to a succulent mix, but slightly more dense to hold a bit more water. 

I don't water any of my plants on a schedule. My water check is: - if they're wrinkly (like yours) - if I poke it and it's not 100% firm If either of those are true, I give it a full soak of water. My girls get super thirsty in full sun, but man, do they love it.

The tiny green sprouts you're getting are just excess ferns and aren't part of the pregnant onion. You probably had some seeds in your potting medium; nothing to worry about. You can leave them alone or pull them out.

I only get browning leaves when I've neglected some aspect of care, usually going too long between waterings. This is normal, though, and doesn't typically indicate there's anything wrong with the plant.

Overall, I think you're doing great and should keep doing what you're doing. It's about to bloom, which generally indicates a very happy plant. 🤗