On the origin, the ads indicate the guns are British-made, but if you are concerned, call them and make sure.
I don't now have a Martini, but I have owned them in the past. IMHO they were the best single shot military rifle made. They are faster than any of the bolt actions and most other single shots, and stronger than the U.S. "trapdoor". The only drawback during much of the period of use was the truly horrible ammunition. As it was, they gave a good account of themselves when the odds were anything near reasonable.
The later rifles in .303 were very good and strong enough for any .303 cartridge. I would have to ask about the barrel quality though; British-made .303 ammo was corrosive and erosive right from day one to the end and most of those rifles were "handed down" to colonial troops whose motto often was "shoot today, clean sometime, maybe."