The oil is milky because a lower unit seal is leaking. The shift rod boot is usually the problem with those, they need to be changed periodically and is very easy to change.
Some degree of that discoloring is normal, The midsection gets warm running down the lake and the mineral deposits in the water have a tendency to build up on the Honda paint
If it is overheating you may have melted the water pump housingand/or impeller most likely because you didnt cover the secondary water intake when running on the flush muffs. There is a plastic screen on the bottom side of the cavitation plate above the prop that you need to cover with a piece of duct tape when running on the muffs because if you dont all the water being pushed in the primary intake will just run out the secondary intake without actually entering the pump. When you melt the upper housing 9 times out of 10 you partially melt the lower housing that holds the drive shaft seals. I would replace the housing and seals too as well while your at it if its the case.
These are both very common issues i see with these motors, the are no big deal to fix as soon as your aware of it.