My thinking tends to scatter and so I have done pieces of things in each of the ages. Then I go back and do another piece after doing other things.

Does it matter if you complete one age before proceeding to another? Can I mess myself up with the game if I do it this way?

And how does one know if they have completed one age? I surely can't tell. Thanks.

It really doesn't matter what order you complete the Ages in, no.

An Age is completed when the Slate for that Age has been returned to the Keep (the large woobly soap-bubble thing you first saw in K'veer, not the smaller woobly soap-bubble things that you link into and out of at the start of each Age). Esher usually shows up and makes a longer speech that goes on in greater detail about Yeesha, himself, and the Bahro.