leaking beer from the output connection
I'd replace all of the o-rings on the kegs.
It is also quite likely that your party tap has a rotted seal. Not much you can do about that.
The door tap might just need tightening.
Remember one unassailable statistic, as explained by the late, great George Carlin: "Just think of how stupid the average person is, and then realize half of them are even stupider!"
"I would like to die on Mars, just not on impact." Elon Musk