7.35x51mm Carcano was meant to replace 6.5x52mm, and both were in production at the same time, as they built up production of the 7.35 chambered rifles. But they had to prioritize in WWII and dropped 7.35 in favor of the larger production base and stock on hand for 6.5.
PPU is the best source for brass. (And 6.5 Carcano brass can be necked up, if needed.) Ammo only comes in about once a year - typically in one of the October and April import shipments. Again, PPU is the best source. Alternatively, Steinel may have some ammo. But they rely on the PPU brass shipment in order to produce their product. So, it comes back to PPU again.
Bullets must be cast, sourced from Europe (not easy, as they're rare there, too), or purchased when in stock at Graf's. Graf's has Hornady produce a .298" 128 gr SP, aka "128 SP Graf's", every year or two. They are generally in stock for 8-10 months after each production run.
It is the only suitable commercial bullet on the market (that I have found) that is anywhere near obtainable.
Hornady and Hodgdon have load data in their "obsolete" categories. Older NRA books have data, as well.
You'll find it very much in the class of .30-30, if not a bit wimpier with US data.
You cannot shoot a Carcano easily without a clip. There are no feed lips in the magazine or receiver, and the extractor was not designed to snap over rims. If you do shoot it by snapping over, you will break the extractor eventually.
You must hand feed into the chamber, while closing the bolt and guiding the rim under the extractor (not easily done), if you do not have a clip. Aftermarket reproduction clips are available, as well as more expensive originals.
Alternatively, there are 3D printed designs for "sleds", "trays", or "followers" that snap into the magazine and allow single-loading and feeding. I have my own designs out there for both 6.5 and 7.35 chambered rifles. There are also some popular designs on eBay, but they over-compress the follower spring, in my opinion.
Your rifle sounds like a Model 38 Fucile Modello 91/38 that was exported to Finland. Those folding bayonets are uncommon - some would argue rare. Guard it and keep it safe.
The 7.35x51mm barrels did not have gain-twist rifling like the 6.5s did. It has a continuous twist rate.
I own half a dozen Carcanos, and have owned more. 7.35 is my preferred cartridge. It is different, kind of dumb, requires a little more attention, and is just a sweet little shooter, even in these light, short carbines. My favorite Carcano came out of Africa, decorated with tribal art and adornments. It happens to be chambered for 7.35x51.
A note on the fixed sight: The battle zero for these rifles (the only zero) was supposed to be 200 meters. For practical purposes related to hunting and sport shooting, however, it is more like 400 meters. Your shots are likely to impact *very* high at the commonly encountered ranges for target shooting.
What did I miss?