impossible potty training

Hmmm ... I've got a Norfolk Terrier/cocker mix, and she's aboutttt a month older than yours, and I had her since she was four months old.  Whenever she peed somewhere in the house, during the first few weeks, I brought her over to a puppy training pad (those blue/white pads with the cloth in the middle and the plastic backing so that nothing leaks) ... lots better than paper.  She caught onto that fairly quickly.  When I would leave her in the bathroom gated while I was at school for 6 hours, I would come home to pee only on the pad.  Still, I brought her outside every 2 hours, religiously.  Since your puppy is significantly smaller than mine, and you're pretty much still starting from the beginning, I'd take him out maybe once every hour.  The point is to get him to associate peeing/poopin with outside.  If you really want him to learn to "go" inside ... follow the trainer's advice and bring him to the paper/pad every hour or so.  Keep a close eye on him.  Don't let him make mistakes without your being able to correct it, because every mistake is a setback, so I've learned.  Gradually increase the amount of time between potty breaks. 
 
If you can't watch him, put him in the crate.  But about the crate.  It needs to be big enough for him to be able to get away from his mess if he must do it in there.  Soon, he'll learn to see the place as HIS space, and he WONT want to mess in it.  You need to decide if the crate's big enough, i'm not sure if it might be too small, unless your puppy is tiiiiny.  He should have room to turn around, lie out completely stretched, and also be able to get away from his pee.
 
Good luck!

I agree with the above advice.    There should be no opportunities to go in the house without you catching him in the act, interrupting and immediately bringing him to the potty pad.   To make this easier, try tethering him to you.

if a dog is peeing in a crate, there is no benefit to using one. The only reason to use a crate is that most dogs are extremely reluctant to potty in their bed and will try their best to hold it. If you have a dog who is willing to potty in his bed, well, crate use is counter-productive, the dog will just happily go. For a dog with this habit, confinement in something like an x-pen or puppy-proofed kitchen with a piddle pad in it will help speed up housebreaking more than continual use of the crate. 
 
Best way to house-break is to never ever let the dog potty in the wrong place via constant supervision and taking the dog to the correct potty place often. Every time your dog has an "accident" it will set you back weeks. If you're really diligent you can housebreak most dogs in less than two weeks. A non-housebroken dog should either be confined or directly in your view (tether that dog to you) every minute of every day, and should go to the potty spot as often as you can manage (every two hours for young puppies, every four hours for older puppies/non-housebroken adults). Yes, even at night. Set your alarm clock. Two weeks of being a zombie due to lack of sleep will pay off big.