we already know that the efficiency of a weapon is obtained through a formula that relates the DPS and the DPP

We don't, somebody told you wrong.

DPS, DPP and efficiency have zero determination one to another.

Efficiency is an absolutely arbitrary parameter of the weapon, handpicked by MA. At the initial installment, efficiency was chosen to be in a direct proportion with DPP, but that doesn't mean they are related. If you read the thread linked by sawachika you will see that the initial scaling used by MA DPP to eff is no longer respected. They used it as a guideline to keep the place in the weapon ecosystem of various already existant weapons.

One vital difference between them is that efficiency can ONLY be increased by attachements, while DPP can be increased by buffs such as +critdmg and +critchance.

The other vital difference is that efficiency affects directly the TT ROI over a sufficiently high enough number of events. And ONLY that. While DPP affects directly the loot composition (what that total TT loot is actually made of).

1) Does anyone have the real formula to calculate the efficiency of a weapon?

There is no such thing, is an entirely arbitrary parameter set by MA. If so they wish, they could release tomorrow a weapon with amazing DPP but 0 efficiency or a weapon with awful DPP but 100 efficiency.

2) Does anyone know how to calculate the overall efficiency of the weapon / laser / amplifier / etc set? If there is a formula about it, what is it?

EFF (set A+B) = ((EffA*CostA)+(EffB*CostB))/(CostA+CostB)

where "Cost" is in the entropiawiki sense, decay+ammo, whatever is spent per shot/swing etc. Obiously in tt terms only. If the decay is L and costs MU, is your place to do the math if is worthy.

Example:

Armatrix LP-55 eff 66 cost 17.2 pec

A 104 eff 82.3 cost 3.039

Eff LP-55+A104= ((66*17.2) + (82.3*3.039))/(17.2+3.039)

= (1135.2+250.1)/20.23= 1385,3/20,23= 68.5 (for actual exact result you need to do the math with 5 decimals and apply the rounding to first decimal)

The explanation of this formula is that:

- each part of the set contributes efficiency adjusted per its impact into the total cost

- because total turnover is made of the total cost and efficiency is strictly related to tt ROI of total turnover

That is why lasers with very high efficiency improve the efficiency with 0.1 or maybe nothing at all, because their actual cost (decay only usually) is extremely low.