Veggie diet has benefits?

Loads of things act as 5ARIs to a minor extent, and there's no point in trying to avoid all those - you'd end up on a very weird/unbalanced diet. It's difficult to find out how much is in these, but if they're not used for reversing recent male pattern balding, there's probably too little to worry about.

The Finasteride dose used for enlarged prostate is 5mg/day, and this is the dose which halves your PSA.
The Finsateride dose used to treat male pattern hair loss is 1mg/day, and I don't know what impact that has on PSA (I don't know if the effect is linear, i.e. proportional to the dose).

Most of the foods/supplements containing 5ARI are not known for having any effect on male pattern hair loss, so I would guess their doses are much lower than the equivalent of even 1mg Finasteride. Saw Palmetto is a notable exception, in that it is effective enough to shrink the prostate and hair regrowth (at least in some formulations), although not as effective as Finsateride and Dutasteride. (Its formulations are also stupidly expensive, much more so that Finasteride and Dutasteride.)

Obviously, I can't assure you which foods/supplements containing 5ARI are safe to take without screwing up PSA readings, but ruling out everything containing small amounts is not viable, sensible, or useful.

Only because of the possibility of generating misleading PSA results, but this would only be with significant doses of 5ARIs.

It takes around 6 months for PSA to stabilise after loss of androgens, and 12 months after restoration of androgens. A few days won't do anything.

As already mentioned, inhibiting DHT has no impact on prostate cancer, only PSA. (There is some thought it might reduce the chance of getting prostate cancer in the first place, but that ship already sailed.) As far as I can see, Biotin is not a 5ARI, but it is sometimes taken with Finasteride to promote hair growth (Finasteride being a 5ARI which is used to prevent male pattern baldness, amongst other things).