hand signals can be whatever you want them to be, just as commands can. The only criteria is that they be clear and consistent. Hand signals should be easy to distinguish from each other and distinct from a distance.
My hand signals for competition, for example, are kind of backwards from the norm. Find one that works for you. My signal for down (Platz) is to raise my right arm and then sweep it down towards the floor.
here are some good links to commonly used signals
http://www.bordercollierescue.org/advice/Content/UniCommands.html
I know people who have trained their dogs in Klingon.
Instead of using a clicker, use a marker word. Mine is "YES" I am dead clumsy and tend to fumble around. Using a marker word instead of a clicker also makes it easier to train on the fly since you can catch and mark behavior at any time.
For socializing, you just need to go out where you pup can see different things. Go into town one afternoon and sit on the bench outside
walmart for a while and watch the world go by. It also doesn't mean that every person you meet should be allowed to pet your dog. Here is a good article on what you really need to focus on
http://naughtydogge.com/blog/puppy-socialization-what-it-really-should-be
For the barking, the easiest thing to do is teach an "enough" command. For any potential problem issue, it's easier to teach a dog to DO something rather than NOT do something. I want my dog to alert bark. He barks; I go check out the noise and tell him "Enough" After that command, I expect no more barking.
Some have good luck by first teaching a dog to "speak" and then adding a "quiet" command. They catch on pretty quickly. This is how they quickly learn to not repetitively bark.
For example, my dog isn't allowed to bark at deer outside the fenced yard. He gives them one or two barks and comes back in. Because he knows from experience that barking at them will get him brought in anyway (we have a doggie door).
He knows not to bark at the neighbors for the same reason. When we get new ones, he does bark at them for the first few days and I look, tell him "Enough" and he quickly learns that these individuals (situations, whatever) are normal and allowed - therefore nothing to bark at.
Rocking your body forward means simply that. You slightly lean towards the dog. It doesn't mean that you tower over them or lean far towards them in a threatening posture. Just slightly leaning your body in their direction. It's actually a natural response when the dog starts to stand up.
Personally, I don't do puppy play times. I prefer to have small play groups with people that I know well and older dogs that I know are good with puppies. But, with doing Therapy volunteering, competing and other activities I need my dog to view class time as "work" time and not be distracted by wanting to play with the other dogs. I also need him to ignore all other dogs unless in a specific situation where we are having playtime.