Sewing machines won't work for sewing patches on your gi. I use a straight running stitch (basting) starting with the knot coming through the back of the material. That way, your thread stays inside the outer ridge of the patch.
Or you can use the overlap stitch (overcast) to keep the patch from curling and pulling away from your gi when you wash it.
You can use both basting and overcast stitches to make sure the patch stays secure.
You'll need a thick needle and thick thread. Or you could take it to a seamstress and have her do it for you. That can get expensive though.
As far as your trousers falling down, that is a common occurrence for all practitioners wearing a gi.
Once you have your trousers on, pull the drawstrings at the sides FIRST. Then tie a double knot with a bow.
Here's a 37 second video deomonstrating how a thin man ties his trousers to make sure they stay up.
HOW TO TIE YOUR GI PANTS 37 seconds