First, no you don't gear for dps as a dk tank for every fight. You gear for tanking, and on certain fights (like Heroic Ultra) you switch your gear up a bit to optimize your dps. Do your healers a favor, stay in tanking gear.
I think someone missed the memo, this is about dps gearing. Yes, you will take more damage, but as someone that can easily do 70%+ of their own healing, I don't think damage is an issue.
Do not worry about gearing or geming for Stamina. This stat will come as you get gear of the appropriate item level.
Stam is a "hybrid" stat for dps tanking, as it provides almost as much AP (via vengeance) as str, as well as giving you a larger healthpool, reducing healer stress. It can be completely viable and reasonable to gear/gem for it. To what extent you gear for it is largely up to you and your healers.
Expertise can be around a rating of 20, do not cap it - it is pointless to do so. Also, you do not need to worry about your Hit Rating at all; mine is at a 1% I believe.
Again, I think someone missed the memo. This is a DPS Tank
thread, we are looking at gearing to put out high damage. This means we want to cap exp and hit.
Expertise is far better than hit until you are softcapped (26 exp) as you can be both dodged or parried as a tank - exp will reduce the chance of either happening. Exp is still valuable after softcap, though not quite as strong as hit.