Well done Bobh! Here is my opinion based upon the sales on ebay these two years and here is something I can comment on:
The denomination of 1762 10 kopeks is a really short lived event, only to be followed by another event in 1796 to be restruck later.
SPM coins in general are relatively easy to find but overstruck 5 kopeks are for some reason more difficult to find. SPM seemed to have overstruck more 4 kopeks. In my collection, which you can check on omnicoin, I have coins of 1763, 1765 and 1766, and they all seem to be from SPM (I cannot read the mintmark of one of the coins).
Now what is more interesting are the mints at that time. Before that time, only MM and SPB were present. In 1763, two new mints were introduced, that are EM and CM. AM was not present during this time.
Now what is more interesting is what Uzedenikov have noted about which mints that overstruck these coins. Ekaterinburg Mint, St. Petersburg, Sestroretsk Mint and other minor temporary mints:
Nizhny Novgorod (bishop's house)
Yaroslav
Porechye village of Smolensk Gubernia
Arkhangelsk
Polotsk
which unfortunately none of the temporarily mints placed its marks on the coins.
One of the key questions is why were there so many temporarily mints created to overstrike these coins. Indeed there are plenty of these overstruck coins, but most of them I have seen are overstruck 4 kopeks, not 10 or 2 kopeks.
Now back to answering your question,
1. Were all of these coins overstruck, or did they also use regular planchets at the St. Petersburg mint in 1763?
I so far haven't seen any of the coins in 1763 that used regular planchets. Perhaps there are, but I am not aware of.
2. If not, do you think mine is overstruck?
Yours seem to be a perfect example of an overstruck 10 kopek although it was quite difficult to make out. I can show you an outline when I have the time.
3. Do you think the edge has been overstruck? There seems to be some kind of doubling of the net pattern on at least part of the edge (I tried to get that in the picture I took of the edge), but that doesn't necessarily mean anything, of course.
Might be?
4. What kind of premium do these coins bring over EM mints, for example? As usual, Krause isn't much help here.
SPB and CM overstruck coins might be rarer although the only overstruck 10 kopeks are the 1788 MM coins... don't ask why I have two...


In general, the price of an overstruck 1762 10 kopeks, 5 kopeks coin is around 50USD or so, as there seems to be collectors who want to buy a sample of such as the original 1762 coin is REALLY expensive! Prices do vary accordingly to the clarity of the overall striking features, in particular, the underlying features as well as the overstruck features, which makes prices extremely difficult to determine. So if you got it way under that, you got a bargain!
Note, the price 50USD is only when the seller does know what he is selling as well as the buyer knows what he is purchasing. There are occasional times when the seller doesn't know what he is selling and hence the low price at times.