Hi & Welcome!
Stitching applique does get easier with practice. I found that starting on a scrap piece for a few minutes helps me get the rhythm just right.
With turned applique, typically, there is no fusible added on the fabric. Cut and stitch it down. You can use a glue stick to hold the applique in place on the background.
Second, it may be the product. Did you use Heat n Bond or the Heat n Bond lite? The LQS ladies recommend the lite product. Another one to consider is misty fuse. There are other light fusible available too.
I would still stitch it down onto the fabric.
Best wishes with your project. Again, welcome to the group.