pKw, pKb, pKa and NEN6411
The impact temperature has on the pKa of strong acids are in practical terms non existent as the equilibrium at any temperature lays very far to the right.

Practically, yes.

The impact of temperature on pKa are more significant for weaker acids.

Yes.

The impact of temperature on pKw is only significant around the point of neutrality. At lower pH's the few hydronium ions produced by H2O + H2O are so few that it bares no meaning on the logarithmic pH scale. In other words, the pH-temperature relationship is important when dealing with neutralization processes, but not so much when having pH setpoints set to anything in the milder acidic region and below.

$\mathrm{p}K_\mathrm{w}$ changes apply to all $\ce{H3O+}$ and $\ce{OH-}$, not just to those from water autodisscociation. If $\ce{[H3O+]}$ ( [] is the convention for molar conceentration ) is determined by $\ce{[OH-]}$, or if some process depends directly on $\ce{[OH-]}$ and not on $\ce{[H3O+]}$, it is significant.

Compensating for the pH-temperature relationship caused by the temperature dependent pKa is only important when doing measurements on processes where the temperature of the process differs from the temperature of the final product and where the targeted pH level during process control has to match the targeted pH level of the end product (at another temperature).
For example: say I want to produce an end product with a pH at 5 at temperature X. In order to make this product the temperature of my fabrication process has to be something other than temperature X. In this case, temperature compensation to account for changes is pKa becomes important - otherwise the end product won't have the desired pH.

Yes. E.g. for acetic acid, $\mathrm{p}K_\mathrm{a, \pu{25^{\circ}C}}=4.75$. That is the $\mathrm{pH}$ of solution acetic acid / sodium acetate in molar ratio 1:1.  Let imagine for illustrative purposes $\mathrm{p}K_\mathrm{a, \pu{50^{\circ}C}}=4.5$. If you used at $t=\pu{50^{\circ}C}$ for the final process $\mathrm{pH}=4.75$, there would not be reached 1:1 ratio.

in a different scenario the pH setpoint of a process becomes a means to an end. It's the pH of the process that determines the chemical reactions that takes place in that particular process (perhaps the hydronium ions merely acts as catalysts). In this case, temperature compensation in no way should be applied. This because the pH changes casued by changes in pkA are real and if the process demands say pH 3 for an optimal chemical reaction then it doesn't matter what the pH would have been at another temperature. The important thing is what the temperature is in the process right here, right now.

Yes, if I understant the paragraph well.

while pH changes that comes from changes to pKa actually do mean that a solution becomes more or less acidic, changes to pKw doesn't result in a solution becoming more or less acidic even though pH changes. This is because an equal amount of hydroxide ions a produced. So only the point of neutrality is changed.

This depends on what you mean by acidity. If you mean by acidity the activity or concentration of $\ce{H3O+}$, it is affected by $\mathrm{p}K_\mathrm{w}$ changes.

If so, then my question now is: What happens when we move into the alkaline region? I mean, pKb is, according to Le Châteliers principle, temperature-dependent as well, right? When looking at this graph https://ibb.co/LRs7G5y (algorithm based on NEN6411 (now DS/EN ISO 10523:2012)) it seems as if alkaline solutions ALSO becomes more acidic with increases in temperature. Why is this? Does it mean that the equilibrium constant pKb runs in reverse of pKa when temperature increases (less OH-)? Or does it mean that pKw plays are much larger importance once we wander into the alkaline region? I don't, however, see how pKw play any importance on the temperature-pH relationship of alkaline solutions. I mean, if we have an alkaline solution of say pH 12, then any extra/or less hydronium ions produced by changes in pKw would be dwarfed by the proportional much larger amount of hydroxide ions.

For weak acids, the primary parameters is $\mathrm{p}K_\mathrm{a}$. Then for their conjugate bases, $\mathrm{p}K_\mathrm{b}=\mathrm{p}K_\mathrm{w} - \mathrm{p}K_\mathrm{a}$.
For weak bases, the primary parameters is $\mathrm{p}K_\mathrm{b}$. Then for their conjugate acids, $\mathrm{p}K_\mathrm{a}=\mathrm{p}K_\mathrm{w} - \mathrm{p}K_\mathrm{b}$.
For solutions of strong acids, $\mathrm{pH} \approx -\log{[\ce{H3O+}]}$,  $\mathrm{pOH} =  \mathrm{p}K_\mathrm{w} - \mathrm{pH}$.
For solutions of strong bases, $\mathrm{pOH} \approx -\log{[\ce{OH-}]}$,
$\mathrm{pH} =  \mathrm{p}K_\mathrm{w} - \mathrm{pOH}$.

The graph you mention is for strong electrolytes, so $\mathrm{p}K_\mathrm{a}$ is not applicable.