What’s new in Microsoft Teams – May update

chico.f chico.f - to answer your questions about general auto favorite, you don't need to set that, you cannot favorite/unfavorite the general channel, it's always favorited, so there is no need for that option on that channel :P. 

As for your 2nd question, you cannot forward messages. The proper way is to @mention another channel and bring those individuals to the channel your posting the message in. This works better because you are not duplicating messages. As for moving it to another private group, that isn't possible, you could get a link to a post in the ... assuming those same people in your private group have access to the message you are linking too. 

Quotes not possible, reply to the original message and @mention someone to bring the conversation to the quote. Otherwise screen snipping works great for that. 

Also, if you have questions about Teams, please direct them here in the Teams community so we can discuss the individual questions outside of this as it's related to a new release update, thanks!