Should the dormer flashing look like this

Everyone has given good advice, but the ultimate decision is probably going to depend on the total cost and real time before you plan to add a full second story. I have done dozens of roofs in my time and can give you the following considerations.

A new roof is probably going to cost you around $300 to $350 per square (10ftX10ft or each 100 square feet) for a complete strip, 6 feet of ice/water shield and new 30 yr shingles. Not knowing the size of your roof and pitch, I can't give you a real good guess, but a simple 24X30 cape with a chimney, no crickets or tricky valleys usually runs around 3 to 4 grand. Any good roofer is going to insist that any damaged or rotting roof shiething be replaced while it is stripped, adding more cost. Don't count on using the old roof structure when you remodel. Raising a roof under a new wall system can be very expensive and I suspect you have an original rafter system and board sheithing. Your new roof will want to be of the newest materials and techniques such as trusses, tounge and grove sheathing, soffit and ridge vents etc. A second story is a huge investment and in my humble opinion, very wise to do it all new.

As far as possible repairs to your old existing roof, you may be able to replace some shingles in the field easily, and repair the leaks around the chinmey with a good coat of blind nailing cement or even remove a couple of feet of shingles and treat the area with Grace ice and water shield then reshingle that small area. Obviously, we can't see or judge the general condition or continued life expectancy of the existing roof. I would strongly suggest you stop the water ASAP as Tester is right on saying a couple years of water can cause you a lot of other problems. Good Luck

That's at the PEAK of a shed roof, true? If that's the case, what you have amounts to a ridge cap, but nobody I know of manufactures premade ridge caps for shed roofs (too many different possibilities, not enough market), so the builder used "drip edge" or flat flashing (bent around the peak) to function as a ridge cap.

There really aren't very many good alternatives to that situation, so what they did is actually pretty common on the peaks of shed roofs. They really SHOULD have tarred over the nail heads, though.