Hi, Eva - the easiest way to determine thread count is to put a pin in the fabric, right next to one thread of fabric, then measure exactly an inch and put another pin into the fabric, then count the threads between the pins. Do it horizontally and vertically, to find out if it is even weave.
I use a sewing machine to neaten the raw edges. Just use a zig-zag stitch right along the edge, or better yet, if you have an overlock foot for your machine, use the overlock foot right along the edge, to that the thread passes over the edge and locks around it. Very easy!
If you don't have a machine, use regular sewing thread (I usually double the thread) and whip stitch around the edges, about a quarter to half an inch apart with your stitches, and going about a quarter inch into your fabric. The point is to just hold the threads on the edge of the linen in place so that they don't pull out as you handle the fabric, and so that no stray threads get caught in your embroidery (esp. on the back, where you might not catch it right away).