People often have a very romanticized idea of what life with a puppy will be like, and the reality - especially when the puppy is an active working breed like a Golden Retriever - can be a bit of a shock.
First, for the crate: Most pups don't like being crated while their humans are in the house with them. Goldens are sociable dogs that like to be with their people and they do not enjoy being shut away in a crate while the humans are in the house. If you're trying to crate-train by putting your pup in the crate while you're at home, you may be setting him up for failure. If you crate him and then go out, he may fuss for a while but should eventually settle. If you've been letting him out of the crate when he fusses, you may have made the problem worse and it will take longer to get past the difficult stage. My advice would be to crate him (1) at night and (2) only when you're going out and leaving him behind. When you go out, don't come back into the apartment unless he's quiet. Have a special (safe) treat for him when he goes in the crate: a stuffed Kong toy would be an example - something that he likes and that will keep him busy for a while.
Second, the house-training: It's important to realize that most dogs aren't reliably clean in the house until they are between five and six months old. The first month is going to be rough. What you have is a canine infant. He isn't physically capable of controlling the muscles that regulate elimination - in other words, when he needs to go, he can't physically stop himself because he has no control over the muscles. He starts to develop that ability around three months of age, and will get better at it over time. In the meantime, just keep doing what you're doing: taking him outside every half hour or so, and giving lots of praise when he does anything at all outside, and watch carefully for signs that he wants to go out (e.g. being near the door, turning in circles). Most pups need to go out shortly after eating and drinking, immediately after waking up, and immediately after a play session. Indoors, when he has an accident, don't punish him: clean it up properly (using some kind of solution that removes the scent) and take him outside. If you catch him in the act, indoors, scoop him up and carry him outside, then praise him when he goes outside.
You should start to see some improvement when your pup is 12 to 14 weeks old, but it's unfair to expect him to be fully house-trained until he's about six months old.
Third, walking on leash: He's a tiny puppy and he doesn't need a harness. If the harness is poorly designed or poorly fitted, it might actually be hurting him or restricting his shoulders so that movement is uncomfortable. My advice would be to get rid of the harness and use only a flat collar. Get a lightweight leash, clip it to his collar and let him drag it around the house for short periods (keep a close eye on him to make sure he doesn't get tangled up). Play games in the house, while he's wearing his collar and leash, so that he gets used to it. Pick up the leash and follow him. Don't jerk or pull on the leash at all. Most dogs learn to tolerate the leash very quickly. Once he tolerates it, he'll be comfortable following you while wearing it. My guess is that the harness is the problem in your case.
Fourth, his name: Names are a human thing, not a dog thing. Your dog has learned some basic commands because when you use a command word - "sit", for example - you always expect the same response from him - to sit down. So you say "sit" and the dog quickly understands what to do because it's always the same thing. It's easy for him to learn. A name is something else altogether. You might say it when you want him to come to you, or look at you, or stop doing what he's doing, or you might yell it when he does something you don't want him to do (e.g. pee on the rug), or you might use it as a sign of affection. So when he hears that word, he knows you want something but he doesn't understand what it is, because you use it in so many different contexts. I teach the name by asking for only one response at first: to look at me. I sit on the floor with the puppy and a pile of treats, and I say the name, and when the pup looks at me, I reward it. So the pup learns (a) that the response I want is for him to look at me and (2) that the name is a positive thing because it means treats. You have to be careful not to use the name in negative situations at first, and always to reward when he responds by looking at you. It doesn't take long if you're consistent. Once he's understood that he has to look at you when you say the name, you can start using it in different situations to get his attention: for example, you can say his name, and when he looks at you, you can give a command: "Fido, come", "Fido, sit", etc.
Fifth, the connection: I find it very telling that you don't mention your pup's name at all in your post. It's as if he's just "the dog" to you, and not "your dog". Setting that aside: the concept of being physically petted is a very foreign thing to a pup. Most pups tolerate it well, but don't understand that touching is a sign of affection from the human. It's something they learn over time. My pup wasn't "affectionate" when he was very young, but now he actively seeks out attention. He'll lie with his head on my foot. When we're on off-leash walks he'll come and trot next to me for a few paces, so I can pet him, and so on. Affection comes when you build a bond with your dog. Right now you don't have that. It's not the pup's fault - he's just being a dog. It's your job to create the bond, not his. Right now you are just his caretakers. It's normal. When you get a puppy, you have to train it and shape it into the type of companion you want in your life. It's not an instant thing: it's a process.
Sixth: I strongly suggest that you find a good training school and take a puppy class. Not the kind of class that's simply a free-for-all play session for the pups, but the kind of class that teaches humans how to train puppies using positive methods. The very best way to create a bond with your dog is to train him. Not only that, but in six months' time your cute little puppy is going to have grown into 60 lbs. of muscle and energy. Now is the time to teach him not to pull on leash, and to come to you when you call him - not when he's a defiant adolescent. After puppy class, you should plan on doing at least a couple of basic obedience courses too. With a large, strong dog like a Golden Retriever, it really is the minimum. Remember, what you have is basically a working dog: Goldens tend to do better in life if they have a job.
Many people aren't prepared for the huge amount of work it takes to raise a puppy and are shocked when faced with the reality. You're not alone in feeling overwhelmed, but you do have a choice to make: either buckle down and do the work, or re-home him quickly, while he's still young. If he comes from a good breeder, your contract will state that you have to return him to the breeder if you decide not to keep him. If you don't have that type of contract, or if he comes from a less-than-stellar breeder who won't take him back, or if you bought him from a pet store, the best way to rehome him would be to contact your local Golden Retriever rescue and ask them to identify a good family for him. Whatever you do, don't sell him on Craiglist or via the classified ads. If you do that, there's a better than even chance that he'll end up as bait for a fighting dog ring, or in a laboratory somewhere. Find a rescue group and let them rehome him.
And last, a dog is a lifelong commitment. Living with a dog in an apartment means taking him out several times a day, every single day, and making sure he gets plenty of exercise. A young adult Golden needs a minimum of an hour's exercise per day - not just walking on leash, but aerobic and mental exercise: training, running, retrieving tennis balls, etc. Or a sport like flyball, agility, scent detection and so on. Having a dog means missing out on after-work drinks with colleagues, or spontaneous weekend activities, because you have to go home and take the dog out. It means making lots of adjustments to your life to accommodate him (vacations, activities, etc.). It truly is a lifestyle choice.
You can do this. It absolutely does get better. But you have to want it.
I wish you good luck with your pup and I hope things work out for you, and for him.
Ruby 13-01-2007 to 18-03-2015.
My dog of a lifetime. I'll miss you forever.