Let me start from your next to the last question:
... the best proxy for "Russia" is the Russian Federalist Soviet Republic. Is it comparable to today's Russia?
Yes, it is compatible to the Russian Federation of today. There are a couple of exceptions.
In 1941 Russia had not:
- the Kaliningrad region (the northern part of East Prussia, which was incorporated in 1945);
- Tuva (which joined voluntarily in 1944);
- the Pechengsky (Petsamo) region (which has rather complicated history of Finland/USSR affiliation, but it seems that the last time when some of its lands were transferred is 1947).
- the Karelo-Finish SSR, which was a standalone republic of the USSR, that is not a part of the RSFSR, but today it is a part of the Russian Federation.
Also depending on one's attitude to the Crimean referendum and the subsequent events one can say that today Russia has not the Crimea as its part, but anyway Russia had it in 1941.
Also one should take into consideration that the borders of Russia with Ukraine, Belarus, Estonia and it might be Latvia are not demarcated, so there is no "inch precision" on the land.
Next.
Or is there a better definition of Russia (perhaps with the benefit of hindsight) for the purpose of this question
There are innumerable definitions of Russia, and which is the best is greatly dependent on one's political views. Even a definition with some ethnic approach is very unreliable and slippery, if you want to follow this way, good luck, if you find any sources which you will consider trustworthy.
So let me stick to the definition of Russia as the Russian Federation of today (including the Crimea), except those parts, which were not parts of the USSR in 1941, that is the Pechengsky region and Kaliningrad one, because you asked about "Russia" of 1941.
How much of "Russia" (of 1941) was occupied by the Germans at
... its maximum extent in December, 1941 and/or 1942?
This is what was occupied in 1941 (the red hand-drawn line) and liberated during the counter-offensive in December 1941 - April 1942 (the green hand-drawn line). The lines were drawn according to the map itself, which is not 100% accurate (at least, I have spotted the absence of the Izyum salient and the Kerch peninsula in the Crimea is not marked as liberated, though it was in the late 1941). The orange hand-drawn line is the current borders of Russia including the Crimea and excluding the Pechengsky region and Kaliningrad one. As a sidenote to that map, the other dark blue part of the map to the east of the red line is what the Germans captured in 1942 (including Sevastopol and the Kerch peninsula in the Crimea).
How much of "Russia" (of 1941) was occupied by the Germans at
... after the successful conclusion of the Russian winter counteroffensives? (Please use Germany's March 1943 recapture of Kharkov as the end of the Russian 1943 counteroffensive.)
This map shows (besides other things) the 1942 German advance (the red hand-drawn line) and subsequent Russian counter-offensive until the German recapture of Kharkov in March 1943 (the green hand-drawn line). The orange hand-drawn line is the current borders of Russia including the Crimea and excluding the Pechengsky region and Kaliningrad one.
Is it true that occupied Russia was "small" compared to the rest of the occupied Soviet Union?
If you mean "small" in the meaning of the area, you can compare these using the maps, sorry I failed to find any reliable source with numbers. The large part of the RSFSR was occupied in 1942, but it was a much shorter period under occupation (7-8 month), than Belarus, for instance, had (three years), so I suppose Germany was not able to exploit these lands to such extend, as it did in the western parts of the USSR.
If you mean "small" in the meaning that Russia suffered less in the war, than other parts of the USSR, I'm afraid it is hard to give an answer without political bias etc. Despite that (in my subjective impression) in our historiography the harshest occupational regime is considered to be installed in Belarus, some parts of today's Russia suffered a lot, like Stalingrad or besieged Leningrad. Also other parts of the USSR which were not occupied (like Uzbekistan, Kazakhstan, Turkmenia, Tajikistan) provided their own effort and suffering for the victory.
Hope, that has answered your questions, the next are original maps without my hand-drawn lines: