Are risks (hexavalent chromium) during Chrome plating temporary, or remain with the product?
Multiple questions should be broken in multiple items, but anyway,

If your plating process is well done, and everything is thoroughly cleaned after, the level of Cr(III) or Cr(VI) remaining should be low enough to be inconsequential to health and the environment. You're correct stating that regardin chrome, thre will be only a passivated layer of metallic chromium and not the trivalent or hexavalent.

Please do remember that the main reason that chrome plating makes things resistant to corrosion is that as soon as chromium is exposed to air, it forms a very thin layer of chromium oxide attached to the surface of the metal, preventing further corrosion. So, in fact, there is some Cr(III) on a finished piece of chrome plated material.

We aren't considering the environment were the finished part will be exposed/used. If aggressive enough conditions are present, the chromium layer will be corroded away and will enter the environment as Cr(III)/Cr(VI).

Regarding Cr(VI) detection, there is a "simple" method involving a solution of diphenylcarbazide described at https://www2.mst.dk/udgiv/publications/2009/978-87-7052-987-7/html/kap04_eng.htm

However, one can easily buy test kits for Cr(VI) on Amazon, ready for use, starting at about (February 2019) USD 110.