The first cartridge, a .357 Magnum, is legitimate. We used to sell it in our store. A dear friend of mine from Germany was visiting, and when he came down to the store with me, he went thru our stock ammo for things to buy, and when he saw the Geco BAT rounds in .357, he was almost incredulous. Seems because that type of ammo was basically illegal in many European countries, including Germany, and also because of the caliber, way more popular in America than in Europe, he had never even heard of this caliber being made in the BAT type.
The second round, an Israeli .45 Auto cartridge, is just a standard target loading, probably with a 185 grain bullet. That is quite a normal FMJ Semi-wadcutter bullet, sometimes referred to, erroneously in my view, as “.45 Wadcutter.” It is a very popular style in the USA especially for match-shooting, as it will feed in the Colt/Browning pistol, sometimes even in pistols with unaltered chamber mouths, although it was quite regular, in the accurizing process of building a real match gun, to open the mouth somewhat to improve function, as many pistols would jam with these ammo loaded with these bullets due to shape and overall cartridge length. Today, most of the better .45 Auto-caliber pistols come from the factory with the mouth already shaped for semi-wadcutter (helps function with many hollow-point bullets as well), since properly done, it in know way changes or hurts the function of the pistols when used with the
230 grain FMJ RN ammunition.
I have not seen the Geco with the odd bullet, that appears to have a brass half-jacket that barely shows about the case mouth. I don’t know what it is. Geco and MEN of Germany have produced a huge amount of bullet types in this caliber, many of them experimental, and that’s about all I can say about it. Perhaps Lew Curtis will chime in and gives us both a real answer.
I don’t know what to say about the Fiocchi frangible. I have not checked my collection, but I seem to recall the odd, “semi-military” dated headstamp is found with this bullet. It is simply a frangible-bullet cartridge, as you said yourself. The red primer seal usually denotes a lead-free or reduced-lead load on Fiocchi pistol ammunition.
I hope this is of some help, anyway.