Secondly, let Kato Kiyomasa drown at crossing the Tumen River - or be killed just before then - so that he doesn't attack the Manchus (what led to the ultimate defeat). Not sure if the defeat was due to the soldiers who had left having gutted the army leaving him with a skeleton crew, or if it would've happened regardless of how big his forces were.
Given that the only thing the Jurchens did was give the Japanese force of 8,000 a bloody nose and didn't participate at all in the war afterward because the Chinese and Koreans rebuffed their offer of joining (on account of them being filthy barbarians and all), I have no idea how this piddling little battle led to Japan's defeat.
What effect would either of these have on the Japan? Would there be a Japanese empire? Or would Nurahaci and the Manchus still get involved? What would this mean for Japanese isolationism?
Hideyoshi's death: little to none. The second invasion had already been contained and was going nowhere when Hideyoshi died.
Kato Kiyomasa's Jurchen adventure had basically zero impact on anything of any relevance, so I have no idea why you bring it up.
As for Japanese isolationism? Well, I don't know about that, but I do know that the realistic outcome of Japan getting a toehold on mainland Asia is:
1. #CurrentDynastyName tells Japan to pay tribute and be good, brotherly neighbors.
2. Japan refuses.
3. #CurrentDynastyName attacks the Japanese toehold and dislodges them from it after some fighting, probably with the help of lots and lots of local guerrillas since the behavior of your average Japanese soldier on a good day in the Imjin War was a cross between the IJA in Nanking and the Dirlewanger Brigade in Poland.
One major effect might be that, given a long enough naval war with an insistent-enough Japan, China would place more importance on actively clearing the seas of pirates instead of doing sea bans, since the pirates have gone from being a passive nuisance to maritime trade to an active military threat, since their bases are dotted all over the Japanese coast and they are basically outriders for the Japanese military. And after that, it only takes a little bit of rewiring to turn a defensive fleet into an offensive and exploratory fleet akin to the Royal Navy.