1) The linen coats I've seen didn't have interfacing, from what I could tell. I also made a linen frock without interfacing, and after a good pressing and starching, it keeps its shape for the most part. If you do want to use an interfacing, I'd use a lightweight linen canvas, possibly even using the same linen you're already using.
2) I would pre wash the linen before cutting either by hand or machine. This will soften the fabric and make it slightly less prone to wrinkles. It supposedly strengthens the linen as well. You can read more here: http://www.trimfabric.com/linen.html
. I do starch my linen coat before wearing it, as the starch helps keep things in place and helps repel dirt a little.
Hope this helps,