Lets start with the OP calling his BA first. Also not every grievance makes it to a hearing....
No it doesn't. But if the grievance lacks merit, than the BA should have informed the OP in a timely manner that it will not be heard.
If it is a grievance to be heard, 4 months is ridiculous. Call your BA and see what the problem is.
If you get nowhere with him, call the local president. If your BA is the president, ask him to do what you pay him to do and schedule the hearings.
Labor charges are a last resort and could have some very serious unforeseen consequences. And I'm not talking about on the union side.