I generally do not recommend introducing dogs with a gate or other barrier between them, as that can cause/increase "barrier frustration" - the same thing that contributes to dogs barking at people from crates, cars and behind fences.
Many dogs also have difficulty meeting other dogs when leashed because they know they only have 6 feet of space - "flight" has been removed, so "fight" is all that is left to them if a problem arises. A dog with confidence issues may give a threat display as another dog approaches so that that dog will say back, thereby avoiding the problem all together.
When I need to introduce two dog that have difficulties like the ones you are describing, I try to take them for a walk in a neutral place so that they can just get used to each other without direct contact and without being on anyone's "home turf." It's non-confrontational and after a while you'll get a sense of how the dogs may react to each other when they actually meet.
Outside of that, I don't know anything about deaf dogs.