The first one is 正真子福本兼房作 Masazaneshi Fukumoto Kanefusa-saku. I wouldn't immediately consider this a fake because it also looks like it has the Showa stamp on that tang, indicating a WW2 arsenal blade. The choppy inscription is typical of WW2 Seki blades.
The other one - I would say 正義則貞 Masayoshi Norisada, but I can find no other swords with this name when I search for it, so that sends alarm bells off.
The first one, Kanefusa, turns up a few hits on auction sites, and I found one registration certificate with this name on it. Normally, if I get nothing but auction site hits, it tends to mean that a suspicious name is getting reflected back in the hall of mirrors of auction sites. Usually you would want to see the name appear in a reference guide or appear on the sword being sold from a reputable dealer. So I am not 100% convinced the first sword is genuine, but the Showa stamp (it has the character 昭 inside a cherry-blossom) indicates the sword was made in an arsenal. These aren't normally faked because they are not worth as much as antique "samurai swords" (for want of a better word). WW2 arsenal swords are not traditionally-made, but collectors of militaria like them. Look on the site below for more info. Yours looks like it has had an amateur restoration job done on it. The sword is OK, but the scabbard is a very damaged WW2 scabbard, and the pommel/tsuka and other fittings are not WW2 fittings. Military Swords of Imperial Japan (Guntﾅ)