It wasn't a trans-Pacific invasion. They already had lots of troops fighting the American communists, and were initially invited to help Mexico in Baja. Then they fell out with Mexico and someone decided to raid the Mexican 'mainland' that proved surprisingly successful and gained conservative support. Tokyo finds it a headache though.
Support...why? The Japanese conservatives weren't the Zerg: they had _rationales_ behind their expansionism, and I have trouble seeing what objectives this invasion of Mexico supports. And they may have a beachhead, but it's still a trans-Pacific invasion unless the Japanese are somehow manufacturing new ammunition, machine parts, fuel, etc. in Sonora. But meh. I don't want to nitpick a nice map too much, and I lack the energy to keep going on this.
Re the other point: I am aware the Germans don't want to go to war with anyone right now, but that doesn't mean the Entente will agree with them, and the Entente is a common enemy. And if the Entente manages to salvage a rump right-wing US, the mutual need will be strengthened. (Given how much of the core industrial areas of the US are already held by the Reds, an outright defeat of the Revolution seems unlikely at this point.)
Bruce