I have been passively shopping for an FX50 for ages, and I am getting really close to buying one now.
Anyway, I wanted to say that in my research, observation of the few online-active 5.0 owners along with my experience with Nissan V8s; I believe you have a faulty engine that would need some extensive mechanical intervention to get close to perfect. I don't know what your mileage is, but I have no doubts that it will keep running up to 300k as long as you never let the oil go too low to cause some other issue. But then consumption might be as bad as 1 qt/250 miles

. just kidding, hopefully not.
I don't think it's your fault, and neither can I specifically point fingers at previous owners, because for all we know the engine might have been an oil burner since day 1 and noone noticed until you came along.
From the 4.5 engine side, 1 quart per 1,000 miles seems to be the worst end of the spectrum - still quite a common number for those who voice their issues. I have known a few (very few) people who decided to replace their engines because the consumption was that bad. However, the vast majority of owners with that level of oil use decide that it is more economically sound to keep adding oil & diligently keeping an eye on the dipstick.
***
Water leak inside or outside? Because outside could be very well your AC system draining condensate.