Full disclosure: I say this as someone who knows next to nothing about tires/tire pressure/cars in general. My tire pressure light has been on for at least three months now.

From https://www.theaa.com/driving-advice/safety/tyre-pressures

"Under inflated tyres will increase stopping distances and affect your vehicle’s handling so that collisions are more likely; Under inflated tyres will flex more and get hotter, making sudden tyre failure – blowouts – more likely; Under or over inflation increases tyre wear so you’ll have to buy new tyres more often; Under inflation increases your tyre’s rolling resistance which means higher fuel consumption"

Maybe worth getting that checked?

The added inertia would provide more shear stress in the rubber to get the tire accelerating. That could have a lifetime affect due to crazing in the polymer/fiber network (which can be especially prone to failure due to interfacial failure between the solid fibers and polymer matrix).

Your assumption is correct. Tire load ratings are per tire.