If you end up cutting the background, be careful not to cut into the applique piece. (Ask me why I mention this! lol)
You do not have to worry about anything happening to the seams. You cut inside the applique shape and away from the seam allowance. Nothing should come undone because the outline stitching of the applique becomes the boundary seam at that point. If it is a small piece I would not cut anything. Generally, there is no quilting over applique pieces. Quilting is generally done up to the edge of the piece.
Thanks for the warning about not cutting through the applique piece! That sounds like something I could easily do.
I just cut a slit in the fabric, and then use my tweezers to pull it out.
OK my two cents becasue I love to do needle turn applique - like Julie said, you don't need to cut away the background unless it will show through the applique piece - and sometimes you get an interesting effect if it does. Yes you may find the hand sewing difficult with all the seams so be sure you have a comfortable thimble (ask me how I know THAT....). And last - what i do is make the applique shape out of freezer paper without seam allowances. I iron it onto the right side of the applique fabric I want. Then I rough cut about a 1/4" seam allowance around the shape. I then either pin, use a very light basting spray, or hand baste the applique piece to my quilt. I can now turn the edges under right up to the edge of the freezer paper so I get a nice clean line. I peel the paper off when done. I find that the freezer paper piece can be used about 3 times before it refuses to stick. Heres an example.
My goal for this year is to learn appliqué, loved reading the comments and look forward to learning a variety of techniques too. I love your water, I hope you will post your efforts when done.
Just ran across some instructions with illustrations from Mimi Dietrich (!) about how to applique with the freezer paper on the back, which isn't the method I've used but from the other posters and Mimi it obviously it works!
I do needleturn applique by marking my pattern on freezer paper, cutting it out, then pressing it to the right side of my fabric, and draw around the freezer paper, then cut about 1/8" or less around the drawn line. I lay it out on my background, either pin or thread baste to the background and use my needle to turn the fabric along the drawn line. I cut the background fabric behind my applique only because I hand quilt. If you machine quilt, it isn't necessary at all because you won't have difficulty getting your needle through the layers. Happy appliqueing.