Looking for a clear explanation...

[Imp]

As you seem to play mainly MBT dumned down basics of info screen.
split into 4 sections top to bottom

Weapon Data
Ammo Data
Armour Data
Other Stuff related to hiting not killing or general stuff like smoke dischargers.

Weapon Data
KILL - Rating vs soft targets first number is using HE
2nd number if one is for other ammo types generally.

PEN - First number is for HE vs Armour
2nd number is for AP vs Armour

HEAT - HEAT vs Armour

APCR - Sabot vs Armour

RANGE - Has no effect on HEAT & HE but AP & APCR lose penetrating power with range, the number listed is penetration at point blank range. With armour 2nd number is APCR range first the rest.
As mentioned there is a utility you can use to check it but you just develop a feel.
Try firing at targets at diffrent ranges to get an idea of how it drops off.

WARHEAD Bigger is better gives a slight boost to all the above ratings, not that important & dont bank on it suggest ignore for now or can hope adds 1/4 to 1/2 it value.
This is what dictates splash levels though causing adjacent hexes to be hit.

Check you actualy have ammo for that weapon its no good having a APCR rating of 80 if you dont have any SABOT on board.

ARMOUR DATA
The weapon data needs to exceed the armour data to penetrate remembering AP & APCR fall off with range.
HEAT uses the HEAT armour values, if listed as zero they are the same as steel.
All other ammo uses the steel armour ratings.

ERA Two types standard that stops HEAT only & advanced (A in front of the number) that stops everything.
This has a chance equal to the number X10% to stop a round but is reduced each time it works.

So 2=20% 5=50%
But if the 5 stops a round it is now reduced to 4 so has a 40% chance of stopping the next one & so on.

Other stuff
HEAT penetration results vary a lot more than other ammo types. Think of the rating very much as an average it can vary quite a lot above & below.
Other ammo types the rating is close to the max possible.

Over Penetration Results.
If within about 300m maybe a bit more in MBT with a unit with good firecontrol etc these may occur if your hit percentage becomes high enough.
High hit chance assumes targeting a specific part of the target like a hatch so it makes an extra roll, if succesfull you see the overpenetration message. 2-6 extra is normal but I have had 32

Missiles & Artillery difrences
Range 2nd number is normally minimum range if any

Note missiles sometimes list HEAT ammo as AP if only one ammo type listed assume it uses HEAT not AP values.
Also with missiles if in notes says TA thats top attack so it hits the top not the side facing you.

RPGs
As you mentioned them it is quite common for them not to be able to stop a MBT from the front especially in modern times vs main powers.
Say 70 HEAT vs 100 HEAT armour.
Before that though the likes of an RPG7 was dangerous to a lot of stuff from the front.
Flank shots or an assault are the way to go.

WW2
Info tends to become far more important as penetration levels vs armour tend to be a lot closer.
Very few units have a seperate HEAT armour rating, mainly some German gear.
Pay attention to gun ranges some are very short so penetration falls off fast. Also a lot of APCR has ranges less than the other ammo so is not very effective at range.
If you really want to could use the AP calculator but Cross has provided a list of common units & expected results earlier in this thread.