First of all, you DO sound super frustrated. Take a breath (or 3 or 5) and just calm down and try to approach it rationally.
Second, the old saying "a tired puppy is a good puppy" is so very true for these dogs. Exercise and heavy play time is so very important. Throw the ball, or whatever, walk walk, walk, whatever it takes to wear him out. Whatever it is that he loves to run for, do it! We try to get at least one good long play session in when we get home from work, it makes evenings much more survivable!
Third, I'm going through the land-shark phase with Odin (almost 6 months) and there are just moments when I feel like I've HAD it. He either goes outside with the other dogs for a bit or gets crated. So if yours is not being crate trained, I'd seriously CONSIDER crate training for your own sanity's sake. Odin can be SO naughty, chewing on stuff he's not supposed to (including me and the cats and other dogs and furniture). The heavy play time really has helped with it, but there are times when he just needs a time out. If distraction with an appropriate chew toy isn't working and he's maniacally chewing on whatever comes into view, Odin gets crated. Do you have ropes and other stuff that he's allowed to chew on?
Fourth, on house training, watch him like a hawk inside. If he isn't in view, he needs to BE in view. Crating again is a very helpful tool in the house training phase. Odin was supposedly house trained when we got him at 4 months, but it took about a month to really get it solid for us and him. He had/has signals that I have never seen in another dog that we've had.
Fifth, jumping and barking/biting...NOT good but can be broken. For jumping, I cross my arms and turn away, it's the only thing that worked with my last GSD. My dad used to grab their front feet and pretend to dance with them and they didn't like that--to the point where they quite jumping on him. Some people use the "knee up" method, but I've had some bad experiences with that. The barking and biting, that's the whole land-shark thing. I hold Odin's muzzle (he's not a barker unless strangers come in the house) and say "no BITE" with my big voice. If he doesn't cool off with it, he gets crated.
Last and probably most effective, I've started on the NILIF with Odin. Nothing in life is free. He has to do something for everything that he wants. If he wants out, he has to sit, if he wants his food, he has to down/stay first, if he wants me to throw the ball he has to sit, etc. and so on. The minute I start doing this with him, he calms right down--or goes in the crate for 10 minutes. The nicest thing about this is that you can work on training throughout the day.
Good luck...sounds like you have a pretty normal puppy!
Chris, mom to:
Tank (Cardigan Welsh Corgi)
Odin (GSD 8/28/13)
Valentine-our ragdoll cat
Two great skin kids