1. You will probably be abler to use the new cassette with your current rear derailleur. Shimano is very conservative about their ratings and experience has shown there is a fair bit of latitude. BTW, most Shimano road rear derailleurs are rated for 27T max so you are only going one bigger.

2. If the chain only has 600 miles it should be ok with the new cassette. However, be sure the chain is long enough to allow big-big with the new cassette. Going from a 25 to a 28T big cog will require 1-1/2 new "half-links" or, realistically, an additional 1" of chain. If it's too short you must be EXCCEDINGLY careful to NEVER shift to big-big.

3. A Dura Ace or Ultegra chain will be slightly lighter and a lot prettier. For the use you describe, there is absolutely no benefit.

Now, there is a less expensive way to obtain the lower gears you want. Change the 30T granny chainring for a 26T. A 26x25 gear is actually slightly lower than a 30x28 and the cost of the change do so is small. Also, you avoid any chain wear and length problems.

3.