Autodesk Inventor

[#1]

I made an assembly and added cuts on parts at the assembly level, but the part files didn't reflect these changes.

How to update those files with the new cuts?

[#2]

First is there a reason why these cuts were initially placed in the assembly and not in the part?

Second try editing the part from within the assembly and use the "Project Geometry" command within the sketch environment to choose the assembly cuts.

Then when you open your parts up those cuts will be there.  Then it is up to you if you want to break these external references in the part leading back to the assembly or not.

[#3]

See if this still works

http://labs.autodesk.com/utilities/featuremanager/

From the ReadMe

"The FeatureMigrator can reliably migrate an assembly feature to the
part level."