They're all re-built rifles; the diamond mark is one factory re-furbishment mark, as is the square-with-an-X on the middle one.
Most of the markings on Mosin rifles are rolled on the barrel, the receiver being the flat (or later round) mostly blank part on the bottom of your pictures. As such, it is possible to swap a new barrel into an old action at the factory to replace a shot-out one, leading to some incongruities as you've seen.
The first one is very nice: a late Soviet model with a very clear Imperial Russian eagle proof on an old hex receiver, so re-built at a very tough time in the war from anything they had available. Eagles would be found on any pre-Revolution (1917) guns, as well as some for a few years after due to the Civil War and also using up of existing parts.
Not the clearest shots; what's the mark in a box to the left of the serial on the '35? This was at the end of hex receiver production, so it's likely in its original configuration.
The Third is the standard marking for a Tula built in 1924-28:
ПЕРВЫЕ
ОРУЖЕИНЫЕ
ЗАВОДЫ
С.С.С.Р.
В ТУЛЕ
1927g.
Which means
First
Weapons
Plant
U.S.S.R.
In Tula
1927 Year
or something.
It would have started life as a Dragoon rifle, a shortened version of the 1891 model for cavalry. Un-fortunately like most it has been re-built to 1930 specifications (you can see the sight), still better than a regular 91/30 with its nice old markings, but only a little more collectible instead of A LOT.
Good collection.
The repository of all information Mosin is the site:
7.62x54R.net