Can you elaborate a bit on how you could tell the dates and such? I have a number of these and would like to give it a try.
Essentially, it's an archaic system of letter numerals, heavily based on the Greek equivalent (which often comes up in some ancient coin series), and distantly related to the Hebrew system used on modern coins of Israel.
For coins of Peter I dated in the AD calendar (as most of the coins here are), the first two digits are always 1700, i.e. A meaning 1 (in this case, 1 thousand) and a shape that looks like a guy with hands up (it's actually a Greek letter psi) meaning 700.
Some late issues (in the 1710s) skip the A and start with the psi (much like how some other countries' coins could say something like 718 instead of 1718).
If your coin just has the A and psi, it's 1700 (though more likely the next letters just aren't on the flan - those things are tiny, and it's unusual for the date to show up as well as on the OP's coins).
Otherwise, the next letter will probably be the units digit. It can be one of the following: A=1, B=2, E=5, S=6, 3=7, H=8, a L-shaped thing (gamma) meaning 3, a triangle (delta) meaning 4, or a circle with a dot (theta) meaning 9.
(If you know the Greek system - as used, e.g., in workshop numbers on 4th century Roman coins - the only difference is that the symbol for 7 looks more like the digit 3 than the letter Z.)
Finally, there can be a letter I, which means 10; so a date with this letter would start with 1710 (e.g. psi-B-I on the OP's fourth coin is 1712).
Normally, it goes after the units symbol, but I don't recall if that's a 100% thing. If you just have A-psi-I, then the date is 1710.
Occasionally, you can find pre-1700 coins of Peter I dated in the old calendar (there are two of those in the OP).
Those coins will have a two-letter date, the first letter being C which stands for 200, the second being one of the units digits above.
To convert those dates to AD, add 200 (for C) to the units digit, then add 1492 to the sum. If the result is 1700, you have a late 1699 coin (I made a writeup on one of those in the "narrow ranges" thread in the main forum); otherwise, adjust the resulting date by four months, since the old Russian year started in September.
...The above description corresponds to coins from 1696 and later. There's an awful lot of pre-1696 wire coins, some of which can even have dates, but describing all of those possibilities would have made this post an awful lot longer.