Hey, good on growing your own plants!
Fist of all, what kind of worms are you talking about? If they are earthworms then they are fine, actually good for your plant. Secondly you should probably get some fertilizer, I like fish fertilizer although it smells so if they are indoors be careful of that. Also you should probably keep your grass outside in a cool spot depending on your location, it will probably grow better in natural light and grass is usually pretty hardy.
You may want to bury your grass a little deeper but only enough to cover up the brown at the base, I'm not sure why it would be falling over and breaking unless it is too stretched. You are also going to need a LOT of grass to get anything from it, one planter won't be enough. You may want to harvest the grass late summer I believe thats when the alkaloids are highest.
Don't worry about the brown tips just leave them on. Brown tips are not normal though and you probably need to trouble shoot that. Usually it is a nutrient problem or could be a water issue.
Good luck! Just watch your plants, they will tell you what they need.
'Little spider weaves a wispy web, stumblin' through the woods it catches to my head. She crawls behind my ear and whispers secrets. Dragonfly whiz by and sings now teach it.'