cd to a symlink, is the same to cd to original folder?

Almost... The cd and pwd commands will behave as if you are in ~/baz (although you can cd to subdirectories of /foo/bar/baz inside ~/baz, when you cd .. you will be in ~)

All other commands will behave as if you were in the real directory and all permissions will be preserved (of course - that's why we say symlinks have "dummy permissions").

This includes (potentially confusingly) commands with relative paths that extend outside the directory. With the exception of cd, which considers you to be in ~/baz, you must make sure you use them as if you are in the real directory, not the symlink. For example if you wanted to ls the contents of /foo/bar, in ~/baz you could do ls .. and if you wanted to symlink a file in foo/bar in /foo/bar/baz(let's call it kitten) then inside ~/baz you could do ln -s ../kitten kitten