Neat David.

There is a great deal of information in the FAQ section that will help answer your questions
https://lcsca.clubexpress.com/content.aspx?page_id=274&club_id=43784

Regarding the appropriate load, I would strongly advise you to have the gun evaluated by a double gun specialist, checking for cracks in the head of the stock, and consider glasbedding or cyanoacrylate impregnation of the head of the stock. Done correctly, that would afford confidence that you can use shells for which the gun was designed; the Western "Super-X Field" 2 3/4" 1 1/4 oz. 3 3/4 Dr. Eq. shell and the 3" "Record" with 1 3/8 ounces of shot.
Again, there is information in that regard in the FAQs.

Yes "I" is for Ideal, and "London Steel" was the name given the barrels by Hunter Arms. London Steel London steel was introduced for the No. 0 in 1907. We do not have composition analysis or tensile testing on a sample of London Steel but there is no reason to think it was not similar to other turn-of-the-century fluid steels.
This might be of interest
https://docs.google.com/document/d/1dnRLZgcuHfx7uFOHvHCUGnGFiLiset-DTTEK8OtPYVA/edit

The mark on the forward part of the flats is the Hunter Arms Proof Mark symbol.

Finally, a Research Letter might identify the original purchaser of your gun and confirm the factory specs
https://lcsca.clubexpress.com/content.aspx?page_id=22&club_id=43784&module_id=245742

There is also a section in the FAQ regarding period appropriate replacement recoil pads; CSMC carries several
https://connecticutshotgun.co/recoil-pads/