She won't starve herself. If she was eating seed before you picked her up she'll eat the seed in the dishes. She's a young bird in a strange place with a strange human - she's scared. Just back off a while and leave her to it. She'll feel vulnerable when eating and drinking so if you remove one of the scary things (yourself) she'll feel safe to put her head in a dish. It just takes time for them to relax so you'll likely not see her drink for a couple of weeks. Hanging round her staring is predator behaviour so stop it. If you need to you can sit away from her and do something else, just taking the occasional glance. Watch her behaviour and adjust yourself as she progresses.
There's no need to rush into getting her a friend. Get to understand her and she'll show you if a friend is needed by her behaviour.