Let's assume I have my psicrystal take Practiced Manifester and Psicrystal Affinity.
The text for Hidden Talent says that it's not an actual manifester level, and only works for manifesting that one power (unless you actually do have actual manifester levels).
Thus, your psicrystal cannot take feats that require a manifester level to take. It can take psionic feats, but not all of them.
How does thiw work for focuses?
It doesn't. Psicrystals can't take Psicrystal Affinity, but they CAN take Leadership to get a psion/psychic warrior/ardent/wilder
thrall cohort with Psicrystal Affinity, however, but it's a totally different character, and you can't share psionic foci.
Also, could I use Hidden Talent as a Kineticist to learn astral construct?
Yes you could. It adds it to your powers known list as if you'd taken Expanded Knowledge, except it's only available at 1st level, only works for a 1st level power, doesn't require a prior manifester level, and gives you 2 pp. Kineticists even get a bonus for having
astral construct as a power known, as the
energy touch ability on Menu B goes from 1d4 energy damage to 1d6 (although the text is wonky, since it was upgraded badly [if at all] from 3.0). It's not much, but it's something.