This is not printing. It is a type of embroidery called Chenille.
Check local with embroidery shops. It's a rather expensive method compared to printing and you should be able to get minimums as low as 1.
On question 2, anything is possible. This also is not a print. The logo is woven into the fabric. Then the fabric is sewn into whatever it is you are making. In this case a sweater. Usually no low minimums on something like this; at least at a reasonable price.
Check local with embroidery shops. It's a rather expensive method compared to printing and you should be able to get minimums as low as 1.
On question 2, anything is possible. This also is not a print. The logo is woven into the fabric. Then the fabric is sewn into whatever it is you are making. In this case a sweater. Usually no low minimums on something like this; at least at a reasonable price.