Nearly every thread involving the TF2 crew, someone says some shit like "well Soldier is immortal" and apparently that makes it impossible for him to lose a fight, because he'll just come back gradually stronger until he does win. Besides this single panel in the comic I've only ever seen referenced as evidence, what else is there that supports this?

Personally, without more information about how exactly his immortality works, I'm going to assume killing him in a WWW context qualifies as an immediate loss, as we have no basis for how long it takes for him to reincarnate. And as for the strength boost, that's literally completely unquantifiable. For all we know, his strength increases by a factor of 1e-∞. So no, he's not going to win via attrition, and no, he's not going to increase in power at an exponential rate.

As for MvM upgrades, can someone describe to me exactly what they are, how they're implemented canonically, and with proof, quantify exactly what they do for the TF2 mercs? I've seen a lot of offhanded claims about them, that somehow they're a game changer vs the "normal" mercs. With the lack of evidence, I'm calling absolute horseshit, but someone feel free to correct me.