Oh my he is sooooo adorable!
The advice already given---to be consistent--is key. He needs to learn how it's done. If you are trying out different methods he will get confused.
There are number of threads that you can review on potty training puppies---they may be very helpful to you.
If he is in a cat carrier their may still be too much room if he can squat at one end and then lay down right beside his potty spot. Be sure to clean up after his oppsies with vinegar and water to remove the smell. If he keeps smelling his pee he will go back and do it again.
Also, as soon as he gets up in the morning and as soon as you get home he should be taken out to pee. Praise him for going outside too---they like that!
As soon as you see him sniffing or acting like he might pee--run outside with him! This may sound tedious, but it's the effort that's needed to get him trained.
And, be patient. He is only 13 weeks old. He is just a baby. A lot of puppies aren't actually fully trained until anywhere from 6 months to 1 year. I'd anticipate accidents happening until at least the one year mark
Anyways, good luck!! Happy training!