I've been following this thread with great interest.
I don't think a bad HO2 sensor would cause surging like you described.
The lower unit is the only part with oil.
There should be 2 screws, one on the bottom of the lower and one near the cavitation plate.
take a couple pieces of threaded rod and put them in the center bolt holes and use them to hold things in place. Once you have two of the studs in then
You want all the water going through the exhaust as it is meant to. Reason is that it keeps it cool so you don't burn your hoses off.
Not sure if this is the info your looking for but I found a sticker with the drive, transom, and engine numbers on it.
ENGINE. 5.7 GSI PEFS....4012028198....3869059