Welcome to the board. You will learn so much on here.

I think it would be especially meaningful for your mother if you were able to use some of your own cotton shirts and/or pants in part of the blocks you make to surround the pillow panel. If you have some that are older or a little small, that she would recognize from seeing them on you, even better! All you have to do is cut off the seams and you then have usable fabric left from the front sections, the back and the sleeves!
I like the idea of adding an iron-on backing to the original blocks, but would add that a lightweight one would probably serve you best.
Stitch in the ditch just means sewing along the seam line of your blocks. I much prefer the second choice given by CarolynMT which is the 1/4" outline stitch as it is easier than following the previous row of stitching and looks very nice.
You are a dear son to be doing this for your mom and I know she will be delighted!

Oh, another thing I wanted to comment on. You don't have to use the 3 layers for a throw. I almost always use only the top and I add fleece as the backing. This keeps it warm enough that I don't need the batting and also makes it warm and snuggly and soft.

I pin the top to the fleece with wrong sides together, do my quilting, then bind. Another option is the birthing method; put the top and backing together, RIGHT sides together, stitch around the sides, leaving an opening at least 8" at the side or bottom thru which you can turn the quilt right sides out. After turning it, you then stitch around the outside edges and do your quilting or tie it as desired.

I don't have an answer for you but when I read that you hemmed your BDUs I just wanted to say THANK YOU for your service.

Well, I don't have a clue what your BDUs are, but if they mean you are or have been in service to our country, I definitely want to add my thanks along with big huggggggs and love!

I also wonder what BDU's are.

This would be my choice also. Pin your top and fleece to your carpet with the fleece side down, then pin in the middle to hold it and stitch in the ditch. Then sew your binding to the edge, flip to the right side and Elmer's school glue it ti the front side and stitch in place.
Thank you and good luck.

Welcome to the board Luis, and remember NO question is a stupid question and you will receive much help and many ideas from the board. What you are doing is really special.

You're getting some good advice here. I'll be interested to see your finished quilt. I'm sure it will be lovely. If you still need some binding info, these are pretty handy. Good luck!

http://www.heatherbaileydesign.com/HB_QuiltBinding.pdf
http://hartcottagequilts.com/binding

Welcome to this board, Louis. And for the old folks (...........) here on the board, BDUs are fatigues. I have a grandson in the AF, and he called his camos BDUs a dozen times before I had the nerve to ask him what that meant. BDUs. fatigues, work clothes, camos, that's what they are, Grannie.