Weightlessness is a minor problem.
This is the major problem:
Which is precisely what forgotten Project Orion (canceled 1964) would have protected against with a double hull filled with water.
Yup. Radiation. Even around certain planets. Jupiter comes to mind.
Um, probably not.
The nervous system isrelatively speaking, insensitive to rad exposures.
IF you had enough exposure to affect the Central Nervous System to the point of brain damage, the much more sensitive organs of your body would be busy dying first.
This is nothing but fear-propoganda.