I'm not really sure what you are talking about regarding stitch count. Can you take a picture or describe it more? Is this a counted cross stitch kit or does the fabric you are stitching on have a printed pattern on it?
Usually counted cross stitch paperwork comes with the color list, a picture grid with icons that stand for each color, and some instructions. I can't remember what the stamped ones come with off the top of my head.
As for strands:
Each piece of embroidery floss is made up of 6 strands. You do have to separate the strands out so you can stitch with them. http://www.needlenthread.com/Images/Miscellaneous/Threads/Twisted_Silk/Twisted_Silks_05.jpg
Check out that picture to see what I mean. (Not my photo)
My favorite way to separate strands is to hold the thread about an inch or so from one end in my off (left) hand (I am right handed), and sort of poke the tip of it with my right hand. It will fluff out as shown in that picture. I keep holding the bulk of the thread in my left hand, and pick one strand in my right hand. Now I slide my left hand down with the remaining strands while pulling straight out with my right hand on that one strand.
I find that is the easiest way and helps avoid unwanted knots too.
When it calls for one strand, just stitch with one strand. When it calls for two strands separate out two and thread your needle with both. Generally the one stranded stuff is for the little fiddly details.
Do you have a hoop to work your stitching on? Those help keep your stitching even, and prevent wrinkles in the middle of your work.
Subversive Cross Stitch has a very good How To write up if you wish to check it out too. http://subversive.myshopify.com/pages/how-to
Best of luck, it sounds like a neat piece!