My first try ended with a big pucker on the back, but since then I haven't had any problems. I suggest using lots of tape around the edges when prepping it for basting (but don't stretch it, just smooth it out really good first, and then tape so there's no puckers anywhere). I use curved safety pins for my basting method - and my suggestion is to use lots!
No, it's optional. I often add it in baby quilts because I like them to be extra warm. But I've used minky on lap-size and even a twin-size and chose not to add the batting layer. It has a nice weight and drape to the finished quilt without.
YES. I always pre-wash the minky. For the top layer - cotton is optional to pre-wash (I would definitely pre-wash less than designer quality), but if working with pre-cuts or small pieces, I find pre-washing unnecessary. For flannels, I always pre-wash.
I've bought from online quilt shops, and also from my local fabric chain store. I don't find much difference in quality, except that there's a bigger selection in prints available online. I like to work with shorter pile minky better, but have worked with a higher pile (rosette print) and it worked as well (but I wouldn't recommend it for your first couple times).
I've done a an-allover stippling, quilted in ditch, and straight-lined echoing the ditch. All work just as well. Just remember not to pull or stretch the fabric as you feed it through your machine. I also highly recommend using quilting gloves!
And YES, all the quilts pictured in this post have been made by me and have a minky backing.