Each person's gauge is different. Nobody can answer this question for you. You will need to experiment by casting on and making a swatch and comparing it with a hat you did with the double knitting worsted and see if it comes out the same, and then either add or decrease the number of stitches until you get it right. Sorry I couldn't be more helpful, but I would be surprised if anyone else could either.

I've made lots of hats with worsted weight - using only one strand of yarn. I use a k2,p2 ribbing. I'm thinking it was a size 8 needle... I use circulars because I hate sewing the seams. So you just keep going 'round and 'round on the k2,p2 until it gets to the right length, then start the decrease rows, switching to DPNs when necessary.

If you don't already have a "membership" at Bernat yarns, go to the web site and sign up. It's free, with no obligations of any kind. They have a lot of free patterns that you can download if you are signed in. The pattern that "got me started" on knitting hats is the one they show using their Denimstyle yarn. That pattern is written for straight needles, then sewing the seam when done. I did that once - hated the seam, so I've always used circulars since then.