Ignore their dickishness, if not whatever content may be wrapped up in it.

Don't argue with the fool/dick/control-freak/etc., you'll have to stoop to their level and they'll beat you on experience.

Yes, of course. Refute them if you can do it without being a dick. Ignore them if you can't. Even if you never interact with them directly ever again, they'll talk to other people, and you don't want to give them fuel to burn you with.

If you have no stake in the argument then it's usually best to just distance yourself from that type of person. Don't allow yourself to sink to their level.

If you do have a stake in it (financial or whatever) then there are books on the subject, but you can get started by searching "how to deal with difficult people"

I like the response "whatever" to such people. It lets them think you really don't care without being too confrontational.