We have a station called BabyFirst that both of my kids loved from a very young age. It's pretty much all educational so I wasn't too worried about them watching it a little each day as I was trying to get things done around the house.
As far as the sleep, my 2yo son struggles with sleep. We do give him 2mg of melatonin every night to help him fall asleep but unfortunately it doesn't last all night. I do remember when my daughter was 2.5 she dropped her nap and started sleeping better at night. Is that an option?
Toys- She is a great age to start pretend play. We bought the Fisher Price Loving Family mansion for DD 2nd birthday and she's played with it ever since (now almost 4). The house is really big so there are lots of different ways to decorate. Play kitchens and food are another good open ended activity. I know it's generally thought of as a boy toy, but DD also has always liked trains.
