1. A queen sized mattress is 60" x 80" across the top. If they have a pillowtop mattress, I'd give another 8"-12" drop to cover down the box spring, and another 6" on top of that to cover the box spring. Since most beds are raised, a little extra drop never hurts, but I know you're tight on fabric.
Your dimensions suggest that your quilt pattern calls for 27 blocks of each type (9 rows with three of each block per row), for a 6x9 block quilt that measures 48"x72" before your border. I would suggest not doubling the original dimensions, but adding two blocks to each row and adding 2 more rows. In other words, your finished quilt would be 8x11 blocks (44 blocks of each type), and would measure 64"x88" before your border. If you add a 4" border, you'll end up with a finished quilt size of 72"x96". You can get a queen-sized Warm and Natural pre-packaged batting piece to fit the quilt (they are 90"x108").
2. If you take the advice in #1, then you'll need about 1.25 yards of fabric cut into 4.5" strips. If you can find a jelly roll, you need a total of 335" (~8.5 strips 40" long and 4.5" wide). Those measurements have an extra 12" built into them just in case.
I hope this helps, it's a beautiful pattern and I love your fabrics
