I had Unburdened Iron, but equipping full plate still dropped my speed to 15 (just that there was a note that I shouldn’t reduce my speed for equipped armor right next to the 15).
Also, while I see the +2 for adding a shield, I don’t see where the hit points/hardness of the shields are shown?
Finally, I tried adding Drained 1 as a condition, expecting it to recalculate my max health, and it did not. Is that something that would show eventually? Automatic stat updates based on conditions?
That’s correct. Dwarves are 20ft -10 for full plate +5 for unburdened iron.
That’s only if the speed reduction comes from a source other than armor, right?
I’ll double check the math for Unburdened Iron behind the scenes.
You can manage the shield’s stats in your equipment or by clicking on the shield icon there by your AC.
Marking conditions don’t currently affect the character sheet, but our plan is to eventually include calculations for conditions and what we call “Temporary effects” like a barbarian’s rage to make those modifications to your sheet while the effect is active. 
For the conditons affecting the character sheet, it should be quite evident that everyone would like that or it’s pretty much useless as a sheet to use during a game (you can take notes on paper, on a screen it’s harder)
Yes, temporary effects are on our roadmap and are something we’ll be able to work on after all of the class features are supported. The character tools refactor lays the necessary foundation to support things like the Inventor’s Innovations and things like familiars and eidolons, which will be our next priority for the Pathfinder tools once the refactor is out.