Doberman Puppy Behavior...HELP!!

Training will make him better. Putting him in his crate is not training but removing him from the situation. No lesson learned. If need be have him teethered to you at all times. The best would be to catch him right before he is going to jump on the table to give him a correction or block him saying a command like "ah" or "leave it." You could make him sit, go to a spot and sit/down stay for a bit. You can start the training by having food in your hands that he cant have until he leaves it alone. (this is not leave it) Leave it he should not be able to have that particular thing if your going to treat him for this use a different treat. You have to be very consistent. Correcting him everytime. I used to set Kyrah up for these things. Leave food right on the edge of the counter or have food in my hand and move very close to her face with it while walking by. You could train him to go on a certain spot while your child is eating at the table. From what I have read seems he has no structure or set rules. Training here is an all day event. Throughout the day anytime I see an opportunity it is taken. When in the kitchen they can come in and then I will say "out the kitchen." I send them out for a bit then release them they can come in if they want. I do down stays usually once a day on their spots (dog pillows they have in the living room) to practice for when people come over. Waits at the door before we go out. Comes while in the backyard. Clicker sessions for fun or if trying to teach something new. Kyrah helps around the house while I am doing things. Keep him busy. I also am not sure if when you feed him does he have to wait for his food or do you just let him have it? Mine have to sit and wait until released to eat.

The leg hiking I am not sure. I am lucky none of my males have ever done this.

First thing, thank you very much for the replies and welcoming me to the site! I would have to say that I do not train him enough, like I said before I was lucky with our female doberman. She just kind of caught on quick and did what she was told, I did put her thru the petsmart obedience course and she was a bit older. I try to take him for a walk every night and we do play fetch in the back yard everyday. My wife and I do make him sit and wait for his food, he is not allowed to eat until we give him permission. All in all he listens and is a good dog when we are giving him 100 percent attention, its when we turn our back for a few minutes he tries to get into mischief! He sits, he lays down and he will leave a treat if told too, we are still working on stay and he will not jump on anyone unless you tap your shoulders and tell him up. I am active duty military and probably don't train with him as much as I should but I do try whenever I get time. My children love him and play with him all the time as well.

Is he neutered?
Sounds like he is marking his territory, specifically the kids stuff. Marking and full out pissing are the same, not to be tolerated.
As mentioned, he needs to be setup and corrected as much as possible.
But if he catches onto the setups, then a diversion has to happen, as it will be a game too.
Table is a toughy, you could be prepared for a mess and have table testing on legs and soon as he jumps on it and it crashes, give a firm no. .
My first dobe was notorious for searching the counter, so I set him up and layer double sided sticky tape on counter, soon as he jumped up and put his paws on counter I told him no and the tape freaked him out, never again did he do it. Setups often are useful once because they eventually try workarounds.

Dobes are determined buggers especially as a pup, this is what makes them great working dogs but boy they will test your patience.
If they get an inch, they will take a yard. Its the undetected issues that are harder to break because they have gotten away with it.
Right now my 8 week pup, likes my vid cable and he will be told no, he stops and will lick it and do nothing and lay beside it innocent, then when he thinks it's clear will lick and try again. Today he will be setup with Tabasco sauce on it and a firm no.