Many question are exploratory in nature and doesn't fit in well within math.stackexchange rules. So for those questions, are there any sites similar in nature to math.stackexchange but more offer more flexibility?
You have more than the 20 pts. reputation needed to talk in chatrooms here, as @amWhy suggested. At 100 pts. you would gain the privilege to create a new chatroom, but likely there are existing chatrooms suitable for exploration of math topics.
At the risk of shameless self promotion, I used to run a Facebook group aimed at exactly this kind of thing, called >implying we can discuss mathematics. I needed to step away from social media for personal reasons, and also not administrate a large group while working on my thesis, so I handed it off to some avid students who struck me as both good math students and positive members of that community. I'm still in touch with a fair few people from that experience and I would wager it's a good place for this sort of dialogue.