how can I avoid custom access permissions when copying from time machine
A way to copy files which can deal with interruptions etc, that is it will not copy something that has not changed is to use rsync

OS X comes with an old version and it is best to get a newer one from macports, homebrew etc. This can copy ACLs and there is a bug in the OS X one (that is in one of my other answers her or SU or SO) 

The simple copy is (the directory Documents to the current directory)

rsync -rtlA /Volumes/TimeMachine/.../Documents .


-a does several other parameters (-rlptgoD ) -A copies the ACLs
-r recurses into directories, -t preservers modification times, -l copies symlinks as simlinks