Having to tell the Blue Beetle, a super-genius who's been at the business maybe longer than she has not to tell anyone she's Oracle is a bit dumb and condescending.
Eh, not really. It's not about him. It's not like she specifically is worried he can't hack it - she's a completely paranoid neurotic, she doesn't trust anybody to know her secrets. She's withheld an absurd amount from Dinah at that point in her story and if there were a way, I'm sure she'd cheerfully erase Dick and Bruce's knowledge of her as well. Flipping out that Ted knows, particularly since him learning wasn't something she controlled or planned for, is par for the course.
Definitely Batdickery, though, true enough. Ted's got a good heart to see through it.
The fishnets may be classic but they're not exactly the best thing to wear if you're a super-hero.
I find the fishnets outfit annoying for a lot of reasons, but first and foremost for me is that the bright, cheerful teal costume just suits the vivacious, outgoing Dinah way better than the Hardcore Black. Comics are a visual medium, a character's image is supposed to convey that character's essence - Clark should be a big guy to make you think of strength and durability, Wally should be angles and diagonal lines to make you think of speed. But you look at Dinah and you get this black boots, black leather thing and the cultural language of clothing says "cool, slick, laid-back hardass," which is just so weird on a character best described by "fun, friendly, doesn't take herself seriously at all."