most constructs are mindless and gain no skill points or feats.
Because it is an extension of its creator’s personality, a character’s psicrystal is in some ways a part of him.
Hit Dice: As master’s HD (hp ½ master’s)
A psicrystal’s characteristics depend on its master. Its Hit Dice are equal to its master’s Hit Dice (counting only levels in psion or wilder), its hit points are equal to half its master’s, and its saving throw bonuses are the same as its master’s.
Increased Hit Dice
Intelligent creatures that are not humanoid in shape, and nonintelligent monsters, can advance by increasing their Hit Dice. Creatures with increased Hit Dice are usually superior specimens of their race, bigger and more powerful than their run-of-the-mill fellows.
Advancement
The monster entry usually describes only the most commonly encountered version of a creature. The advancement line shows how tough a creature can get, in terms of extra Hit Dice. (This is not an absolute limit, but exceptions are extremely rare.) Often, intelligent creatures advance by gaining a level in a character class instead of just gaining a new Hit Die. (See Improving Monsters.)
By the rules, it is a little dubious, it is a very non-standard creature entry. The entry specifies various variable properties and the feats section is fixed. It seems that the intent is that its feats remain static. As for the rules, well, it never actually uses the advancement rules so feat increases are not really referenced, but it does genuinely gain hit dice, as opposed to familiars which just have a bonus to hit dice against hit dice effects... And then again, the hit dice don't actually do anything, they do not confer skills, saves, or hit points, so it seems clear to me that the intent is that they do not gain feats, and that the text is ambiguous, but probably(according to the SRD) in favour of feats, though both these claims are dubious...
As far as the characterisation of them goes, I would see a strong argument for the psicrystal having the same feats as the master, but that is completely unsupported by the text...
The D.M. says no, and this seems sensible for balance purposes, I would consider including a feat that would grant feats to the psicrystal, psicrystal independence maybe, maybe a feat chain two or three long, first it gains feats according to half its hit dice, then you can transfer some of your power points and known powers to it, then it gains the class abilities psion/wilder of half your level except that it has no power points and instead has to use its master's...
Hmm, I seem to have wandered off again. Feats would be essentially free, and could imbue some pretty significant abilities. I would make the same decision myself for balance and flavour reasons. Psicrystals seem more like storage devices and a reflection of the character's own mind, and less like miniature cohorts and custom pets...