I would only split the cases if you intend to repllace the crank, bearings and seals- no reason to do all that work just to put the old parts back in.
Shifting problem may be bent shift forks or just wear- it is an old bike. Flushing is hopefully going to loosen things up
It may not want to go into nuetral if the clutch is not fully disengaged, check the clutch basket, the tangs that the clutch plates ride in my be grooved or notched, some say thay can be filed smooth , but if you can afford a new clutch basket that may help with the shifting problem.
If you can get someone to do a leak down test on the engine that will tell you how the crank seals are .
Milky oil could be the head gasket or the base gasket too.But is usually the water pump.