Where can I propose and discuss ideas, get more mathematicians involved in discussions and propose ideas on a mathematical problem?
I have the feeling that Math StackExchange is not the right forum for it, because it seems problems have to be more concrete or specific and not a place to have more than just one discussion. For example there are places where one has to be a bit more ambiguous and vague to find new ideas to a difficult mathematical problem. I have lots of ideas, but now I don't want to open a new thread each time I get a new one after some research. (And the research I do is about a specific problem in mathematics).
Now I just found a tag named: "mathematical modeling", can I use that for hard problems and idea and brainstorming/mingling?
In my opinion, live discussions on faculty or during conferences have no online replacement; most mathematicians I personally know have same belief. In isolation from academic society it's very unlikely that you will have possibility for such communication with positive outcome.
I do not know where you live, but if there's a university with decent math faculty nearby, I highly recommend to look for research seminars related to your theme and attend them. (They are usually semi-open to visit, communicating with seminar secretary will probably help.)