Wolchonok,
2. What is the difference between Б, БР, БП, Б3Р, and what do they mean?
Right, this all relates the Russian Armed Forces, well Russian MoD, GAU and GRAU index code systems.
The GAU system was replaced with the later GRAU system in about 1956 for various reasons. As such some of older munition codes from were expanded upon and new munitions moved into revised divisions. For example, new munitions generally moved from Division 53, to Division 3.
For ammo, the GAU system was broken down as such: Division - Type - Originating Weapon - Modifiers. Hyphens present between each, though not normally for the modifier. An example would be the 53-BP-354A means: 53 = ammo; BP = armour-piercing (B) spinning HEAT projectile (P); 354 = the 76.2 mm Divisional Gun Model 1902; A = a cast iron projectile.
The GRAU system was is pretty similar, but it drops all hyphens (though they creep in for some difficult ones), and drops the originating weapon, so making it more secret as you don’t know what weapon it’s for just from its GRAU index code.
Right, to answer the question…
These codes (for Division 53) originate with the GAU system.
Ф = Фугасная граната = High explosive projectile
О = Осколочная граната = fragmentation projectile
ОР = Осколочно-трассируюшая граната = fragmentation tracer projectile
ОЗР = Осколочно-зажигателыю-трассирующая граната = fragmentation incendiary tracer projectile
ОФ = Осколочно-фугасная граната = fragmentation high explosive projectile
БР = Бронебойно-трассирующие калиберные и подкалиберные снаряды = armor-piercing tracer caliber and subcaliber projectiles
БП = Кумулятивные вращающиеся снаряды = rotating HEAT projectiles
БК = Кумулятивные невращающиеся снаряды = non-rotating HEAT projectiles
Г = Бетонобойные снаряды = anti-concrete projectiles
Д = Дымовые снаряды = smoke projectiles
ДЦ = Пристрелочно-целеуказателъные снаряды = target marking projectiles
С = Осветительные снаряды = illumination projectiles
З = Зажигательные снаряды = incendiary projectiles
А = Агитационные снаряды = propaganda (leaflet) projectiles
У = Выстрел натронного заряжания = fixed ammunition
В = Выстрел раздельного заряжания = separate loading ammunition
Я = Ящик (укупорка) = packaging
В = Взрыватель = fuzes
Т = Трубка и т. д. = tubes, etc.
The GRAU system added or modified a few projectiles post 1956, these being.
Б = Снаряды бронебойные = armour-piercing projectiles (think small arms, etc.)
БР = Снаряды бронебонно-трассирующие каморные и сплошные = armour-piercing tracer shot (solid) and shell (hollow) projectiles
БМ = Снаряды бронебойные подкалиберные = armour-piercing subcalibre projectiles
This data comes from a Russian document from 1968 it title roughly translating to the 'Design and Function of Artillery and Ammunition (Shells, Mines, Charges, Shells, Means Of Ignition, Tracers)'.
I'll answer other questions relating to 76 mm APHE projectiles another time. For the mean time, here are some other images. (Such s why the internal cavities were different and what was in them.)

The 53-BR-350A from a 1949 book on 76 mm ammo.

Same book, but the 53-BR-350B.
From an offical Russian military 1971 book on the 76 mm divisional gun M1942 (ZiS-3). I think a boo-boo's been made here as it would seem to be a 53-BR-350B by the look of it.
From the offical 1974 Yugoslav manual on ammo.