1) He usually gets along GREAT with Tita (Cocker Spaniel). But sometimes, when my husband or I go outside (backyard) to get the laundry (our washer and dryer our outside in a little shed type thing), he starts trying to nip her neck (it seems playful), Tita hates that, she reacts, and they start a fight. Is it jealousy? What is it? I can't seem to understand it. We take them out both for walks, and don't have this problem. They ONLY fight under those circumstances. They don't fight over food, they play with each other, Gardel (GSD) cuddles up with Tita when it's cold out. I just don't get it...
From what you wrote, it sounds to me like he is trying very hard to get her to play with him and she is not interested. Don't allow him to nip at her. He needs to respect her boundaries, if she indicates she doesn't want to play, she shouldn't have to. Separate him from her for this behavior.
2) Everytime someone comes in to our house, he kind of nips at their heels and sometimes even their hands, and he jumps up. This might be because lately we haven't been able to spend that much time with him (we're sort of going through a family crisis, and are having a hard time giving him the attention we used to give him). Could this be the reason? Or is he just nippy?
Do not allow him to greet people at the door. If you can, put him in a spare room with a chew when visitors arrive or in the yard. When everyone is in and settled he can greet the new comers. He is still a baby, but he needs to understand what is and isn't appropriate behavior.
3) I go out running with Gardel, but have problems when other dogs walk by. This happens when I go out on walks as well. He goes CRAZY. He starts kind of lunging at them, and does like a high pitched cry/bark. I think he's a bit of a Nervous Nellie, or something, but I just don't know how to help him!! This one time a lab puppy came up to him, he just looked at him, and Gardel suddenly lightly nipped him!!
I recommend BAT training. You want to start with him below threshold, this is before he even reacts to the dog, so you will have to determine how close you can be in order to train. Work on rewarding calm behavior when he sees other dogs. Which may mean, a dog is 30ft away, Gardel is looking (but not hard staring or lunging towards said dog and is def not barking)..then reward. Rinse and repeat. If you do this correctly you will find that if he sees a dog in the distance he looks to you for guidance. On days you don't want to train, do not allow him to rehearse this behavior! Take him for walks when you know there will be no other dogs around, or if you see another dog duck behind a car or turn around and go the other way. Every rehearsal will make the behavior stronger.
Another idea is to create a look at that cue. Do this at home, with little distractions. Say "Look at that", point if you want. He can turn and look at whatever it is you are pointing at (and at this point it could be the grill in the back yard it doesn't matter) and when he turns back to you, reward him. Keep working on a solid "look at that" at home with any object, then work up to people or the other dog in the home. Then use it on walks.
4) I don't know how to help him bond with the new Kitty. Tita had no problems. A bit resistant at first, but now they get along. Gardel just seems like he wants to eat him, and also lunges at the kitty,
He is not allowed to chase kitty, nibble kitty, lunge at kitty. The only thing he can do is calmly look at the kitty. I would be rewarding calm behaviors around the cat (ie laying down, not looking at the cat, sitting)...You could also do time outs for when he does decide to chase the cat, but I find these rather frustrating for some dogs, and you could end up doing 100 time outs in a short amount of time. The way this looks would be that he gets crated or put in a spare room every single time he is inappropriate with the cat.