I would like to stay out of the debate going on below as I do not agree with all of the strategies and suggestions that were given as training tools for housebreaking.
First off, you need to control the marking behavior by purchasing Bellybands for your little guy. I would like to discourage you from using a doggie diapers as they are more for incontinence and females in heat.
What a bellyband does is stop the ability to mark by catching the urine before it hits the mark but it does not stop the marking behavior. Are you sure that he is marking and not having a house training issue? These are two totally different and need to be addressed differently.
Since you live in an apartment, I am guessing that this is a house training issue and that he is not going outside enough. You also need to remove his ability to sneak off and pee and you can do this a few different ways.
Tethering him to your waist is a perfect solution to not allow him to get out of your site. When he is not tethered to you then you he needs to be put into his crate. As hard as this might sound, you need to take him out once every hour and as soon as he pees, praise, treat and back into the house.
Put the belly band back on him and keep him tethered to your waist or into an xpen or crate. The crate needs to be small enough so that he does not have room to potty inside the crate. If he does have a potty accident in the crate, clean it up and DO NOT SCOLD HIM.
Each time that he does potty outside you can let him have a little freedom but until you can totally trust him you need to keep him either tethered or banded. When you take him out you need to make sure that he does his business and immediately afterward bring him back into the house. He does not need to sniff around and look at the birdies. Potty inside, tether or crate, with a belly band.
Is he a puppymill puppy? If he is you need to handle him differently than if you have had him from a baby. Puppymill dogs are use to living in their own filth and many cannot be crated because of the past trauma of the mill.