As for hand piecing, I don't use a running stitch. I, honestly, don't even know what the stitch is called or if it has an 'official' name. I take a stitch through both fabrics, pull thread all the way through, take a second stitch about 1/2 the length of the first stitch, pull thread through, etc. This somewhat 'locks' the stitches. I make relatively smallish stitches when doing this.
As to hand quilting, I don't worry about the number of stitches/inch either. I strive (and notice the use of 'strive' here) to get even stitches top and bottom. I use normally a #11 Roxanne quilting 'between' needle and whatever hand-quilting thread is of the color I want for that piece/section of the quilt. I learned hand quilting primarily by watching Simply Quilts on TV. If you use a hoop to hold your sandwich while quilting, keep it fairly loose in the hoop so you have room to maneuver the fabric. I find it's easier to maneuver the fabric vs doing the traditional 'rocking' movement with my hands.
I've never watched a you tube video of hand quilting but I'm sure there are many here that will jump in and provide you with some helpful links to those.