Como dizer "Estar, ficar de segredinho" em inglês

To situation and sentence #2, could also be:
I hate people who make gossiping around others a daily pastime"
OR "I hate it when people, in cliques, engage in negative/toxic gossip".

I mean, gossip per se could be somehow a way of communication - that´s why you can see gossip magazines and read the newspapers, etc. But it can turn into a mindless form of communication as well. Positive gossip, for instance, could be about achievements, skills of other persons, etc.
When I mention "in cliques" I mean cliques to promote the "ostracizing" (that is, to alienate) other members or because of fallings out with one or another of the group. Not keeping to themselves secrets that were trusted to them or badmouthing (talking bad of) other friends.
"If your friends gossip about their friends with, they will gossip about you with others", so careful with the gossip mill!
My two cents!

Valeu PP
O que me intrigou na pesquisa que fiz foi o hush-hush.
Ex.
Eu temo que ainda vá ser segredinho.
I'm afraid that's still hush-hush.

Eu já traduziria diferentemente:

Desculpa mas isso ainda é um segredo/ainda está em segredo.
Desculpa mais isso algo de que não se pode/não devemos falar. (não é algo que se pode tornar público)

I´m afraid- desculpa, lamento (mas...).
As in "I'm afraid now is not a good time to talk... It's for a phone interview."
Desculpa/lamento mas não posso falar agora, é uma entrevista por telefone.

To hush - to silence, keep from talking,
The teacher said, "Hush everyone, I'm trying to explain."

Hush-hush: secreto/confidencial/sigiloso.
The teacher said, "Hush everyone, I'm trying to explain."

Some examples and explanation from Wordreference (some with a bit of tinkering by me).

It could be a "segredinho" if it was about the wedding in secret, but perhaps one would prefer "segredo" when talking about something related to an investigation or a process that runs on judicial secrecy. It goes with context, similar to "uma mentirinha" and "uma mentira".
Plus, intonation certainly will play a part there as well.