In both Moscow and St. Petersburg, you are taken to large souveneir shops where you can spend a great deal of time looking at jewelry, porcelein, shawls, etc. But the selection, though larger, is no better than that in the gift shop on the ship. And prices are comparable.
Any place that's offering bargain prices on things like amber is out to cheat you. It may be amber, but it's probably plastic.
You will be given handouts describing the crafts available for purchase and what to look for. Also, there will be a demonstration by a couple of the PDs, some crew, and gift shop staff describing what to look for.
In the gift shops, there is a lot of green amber that is very clear and looks like glass. It's not very interesting to look at. I purchased a bracelet on the ship that is alternating squares of green (not clear) and cherry amber. Most amber you see is set in silver. If you buy a ring or bracelet, remember it cannot be re-sized when you get it home. Amber is flammable.
As far as Faberge eggs, someone posted above (or maybe in another listing) about getting a beautiful one on the ship for a better price than others seen in shops.
The Hermitage museum does have one or two gift shops.