Lily would not have been his teacher (oh my god, ONE PERSON she wouldn't have taught, her relief is nearly palpable), but she would certainly know of him.
Tonks probably thinks he's a badass. Her current job is to keep an eye out and guard the Department of Mysteries, so it's totally probable that they've met and are bros. She also thinks he's cute.
Katie would definitely think the oldest Weasley is cute, but is far too shy to have ever said so. She probably mostly thinks of him as "George and Fred's hot older brother." If he's a Quidditch enthusiast, he might know who she is?
Pippa:
Lily got nothin'. I mean, GIRL POWER, but Lily's not setting foot in that place because she has to be a Respectable Mumâ„¢.
Tonks would totally go to the burlesque shows. Oh hell yes. That sounds like good times.
Katie thinks Pippa is beautiful and is wholly terrified of ever setting foot in that place, both because she knows she'd humiliate herself and because she knows the papers would catch wind of it.