I want to know if this is grammatically correct " How long would the conference be for?".
I think it's helpful to rephrase to a statement rather than a question...
1: The movie is two hours
2: The movie is for two hours
3: The movie lasts two hours
4: The movie lasts for two hours
I could just about tolerate #1, but #2 is completely unacceptable to me. I've no strong feeling about whether for should be included in the second pair, but certainly in OP's exact example that would be perfectly acceptable once be is changed to last.
It should be, "How long will the conference last?" "For," in this case, doesn't refer to anything - if you said (for example) "How long do you need me to hold an object for," for would refer to the person asking you to hold the object. Since the you are not holding the conference for someone, you to do not need to add the word "for" to it.
I don't remember why "be" is the wrong wrong ending as well, someone else can tackle that.