Yes, both western links can be built (why do you think they provided two western link hexes?). Note that the western link belongs to the building player (you put a marker on it) and does count towards either the most links or the longest railroad tycoon card.
The rules explisitly say that ALL red cubes delivered from a western link city to Chicago cause two new cubes to be added to Chicago. So yes, any red cubes already on the city when the western link is built or even those added afterward (via New Industry or City Growth) also work.
Thank you, I have been playing correct, but wanted to make sure. I was challenged on both rules tonight, and my rule book seems to be missing.