Do you get 2 coins from Xenophon for yellow cards put into play by Halicarnassus/Solomon?
Yes for both. "Build" is just a short, thematic word for putting into play.

On p. 4 of the rulebook, it states:


  player will get to build structures (cards)


and a bit later on:


  Some cards have no cost and can be put into play for free.


(using the Eastern Trading Post as an example.) The same page uses "construct" as another synonym. ("Some cards have a resource cost. To construct them, the player must...")They all refer to the same thing.