When I was at houston, I picked up a fantastic book by Cynthia England on how to create paper piecing patterns - how to create your own. The technique is easy, and though it's meant to create full pictures from photos, I can see how it would be easily applied to simple drawings as well - have a look here - http://www.englanddesign.com/books - best of luck!
For piecing and small quilting (less than 20"x20"), I have a bernina 440 QE - I'm thrilled with it, even if it is out of time right now with a 6 week wait for a repair. It was about $3500, and had been used at a trade show. Had I to do it over, I'd get it again - it's been fantastic.
For large quilting, and because I'm a spoiled brat, I have an APQS Millenium. If you're intending to do quilting as a business, I'd go for that - the thing is built like a tank. That being said, unless you are also a spoiled brat, you will likely have to take out some kind of a business loan to get it.
Rather than the 7/8ths thing, I break out my time/money/quality triangle, and go with time and quality for a change. I up the measurement to the whole inch, and then trim back down - I find it goes MUCH faster and is MUCH more accurate when the final cut is made.
You shouldn't need to fuse it if you're going to stitch in the ditch, but you will need to lay it out flat and "baste" it with safety pins, just to make sure everything moves evenly and you don't end up with a bubble at one side or 'tother.
I'd lay the backer flat over the top, then sew around the outside and "birth" it through an opening. Without *something* holding the layers together, though, it will behave more like one giant bag. There are a few things you can do. You could tie it at the intersections, and then bury the threads (this is minimally noticeable on the front, and only marginally so on the back). You could straight stitch in the ditch along the grid, same deal, only trickier. In order to keep the two layers close together around the edge, you can edge stitch, basically topstitiching a certain distance away from the edge (a quarter or a half an inch). The last one is probably best used in conjunction with one of the first two, but it *will* keep it together more than nothing.