What is a kernal?
First time I flashed, I booted into upload mode and used odin but every time after that I just used rom manager. I do recommend making a backup in CWM if thats is the recovery you decided to go with. I also recommend a wipe and flash. My first time I dirty flashed and had success but you arent gonna get any advice to do it that way.
Could be your samsung driver. I had to use an earlier version for my pc to see my phone. You could download it straight to your phone if you're on wifi. Also, who is your carrier? Just want to make sure I steered you to the right rom. You could soft brick if you flash a rom not for your device.