Many thanks, rod! Continuing:
10000 rubles
Genuine. A&T say nothing in the notes I have, Barefoot gives rather vague points. This example is clearly in the color range of genuine stamps ("flesh", per Barefoot) and is probably an earlier to middle printing. If there are any frameline extensions and square corners, it's a sign of a genuine stamp. The left and bottom panels meet in a curve. The decoration second from the bottom of the left panel is a 3-lobed leaf.
The window behind the woman's head is well-formed; the left pane has fairly sharp corners and shaded. There is also a white dot located relatively high on or above her head scarf. All this is noted since plate wear could obscure some of these points. The child's head is badly done as on the forgeries.

Forgery. A bead has been added where the left and bottom panels meet. This may not be true of all forgeries. The 3-lobed leaf in the genuine is now unrecognizable. The panes in the window behind the woman's head are now heavily worn and rounded. The white spot on/above the woman's head scarf is now at the back of her head.

Forgery. Characteristics are those of the forgery above. There are also dots and blobs outside the right frame, a clear sign of photographic copying and a telltale of a forgery for this issue.
Once again, there are margin scratches in the genuine and in fact the frameline extensions are remnants of printer markings used to lay out the stone (plate). Individual genuine stamps will have different markings (if any), but it appears that certain forgeries are only found as only one copied design as they have the same marginal dots and blobs as well as other design characteristics.
15000 rubles 
Genuine. There is a small spur in the outside frameline below the fish's "necklace" (A&T, Barefoot). Note the shape of shading at the top of the body of water; this is a Type 2 printing characteristic.

Forgery. No spur (A&T, Barefoot). Barefoot notes a closed curl on fish's "nose" which I think refers to the second curved line making the "nose" look like 2 nostrils. Barefoot also notes the white highlights on the water is a "compromise between Type 1 ... and Type 2". The white highlights are actually large blobs along the top edge of the water on this typical forgery type.

Forgery, soft white paper. No spur. The fish's nose appears correct. The highlights on the water are slightly different from the genuine Type 2. This has the typical dots and blobs outside the framelines for this type forgery.

Probable forgery. This looks to be a very worn example of the very scarce Type 1. Type 1 has the same spur as Type 2. In Type 1, the upper third of the water is white/unshaded. Also, the upper left corner of the sky has dotted lines that appear to be retouching; Type 2 is just white in that area.
The sky corner in this example has a few remnant dots and the water has a little more shading than is visible here. The key frameline spur exists. So, these are correct characteristics for a Type 1. But this is on medium white paper with thin clear dull gum (disturbed), so it is not the genuine stamp.
20000 rubles
Genuine. Frameline extension at upper left (A&T, Barefoot). Further, I note that the ribs of the "feathers" are neatly drawn and well-defined.

Forgery. No frameline extension, though some forgeries might show a trace of an extension. The "feather" ribs are sloppily done.
To be continued.