If Poe is close enough to Esege to treat his focus as his own... would that be considered having one, or is it only when spending?

No, as long as he's close enough and attacking it should count.

I'd disagree. Poe's ability reads "if you have..." while Esege's ability says "may treat your focus token as its own." To me, Poe's ability demands that a Focus token has been physically assigned to his ship at the time of the attack. I believe that when another pilot is "using your [Esege's] focus token as its own" it is doing just that, spending the focus token from Esege's ship, not stealing the actual token and assigning it to its own ship. Maybe I'm splitting hairs.

Yep, you're reading more into it that's not really there. It says merely treat them as your own. It doesn't stipulate having to do this only when you need to spend one.

No, as long as he's close enough and attacking it should count.

This seems correct to me. As long as Poe is in range of Esege and attacking (per Esege's ability wording), then he treats Esege's forcus token as if it were his own, which triggers his ability.

We'll surely if it would trigger during the attack, then it would trigger during the defend.

We'll surely if it would trigger during the attack, then it would trigger during the defend.

No, because Esege's ability only works when the friendly ship is attacking, not defending.