Why does Armor Penetration have anything to do with Toughness?
Armor Penetration should be used to calculate how much damage penetrates Armor.
A weapon should gain 16.7% penetration if its AP matches the enemy's Armor Save, the pen increasing an additional 16.7% for each point of AP above the enemy's AS.
Plasma Gun with AP2(5 of 6) should have 33.4% penetration vs a SM's 3+ Armor Save(4 of 6).

Strength should determine weapon damage, while Toughness should determine character HP and damage resistance.

Spoiler

Being a scale of 1 to 10, each point of Toughness should be 10 HP.
Each point of Strength should be 3.4 DMG*.
For each point of S above target T +10% DMG
If S is 2x or more than target T +50% DMG
For each point of S below target T -10% DMG
If S is 1/2 or less than target T -50% DMG

Plasma should not have any special qualities that help it kill higher T targets quicker. It should merely be the fact the weapon has high S that it can still kill high T targets quickly.
Bolter TTK vs CSM should be: 1.75-sec, 8 Bolts, 0.25-sec Fire Rate
vs MoN CSM should be: 2.25-sec, 10 Bolts
Plasma Gun TTK vs CSM should be: 1.05-sec, 4 Shots, 0.35-sec FR
vs MoN CSM should be: 1.4-sec, 5 Shots

Bolter TTK raises by 0.5-sec, PG by 0.35-sec.

*Imperial Guardsman(Human) is Strength 3 and used for 10 Base DMG. System rounds DMG to nearest 1/10th so each point of S must be at least 3.4.

No. Armor would remain exactly as it is. The only thing that would change is that Armor Penetration would allow damage to penetrate your enemy's Armor in order to wound their HP directly.

The Bladestorm rule, which is identical to the Rending rule, was a 1/6 chance to ignore the enemy's Armor and automatically Wound them.
In EC, it can instead be 16.7% AP against all Armor types, causing 1/6th of your damage to ignore the enemy's Armor and automatically Wound them.

It's actually incredibly simple.
If Armor Penetration matches Armor Save, 16.7% of the damage bypasses Armor. 16.7% additional damage gets through for each point above AS.
For example: Plasma Gun with AP2(5 out of 6) would have 33.4% penetration vs a SM's 3+(4 out of 6) Armor Save.