That really depends. There is no simple universal answer.
If your entire drive is part of your user space, then it makes sense for you to own all files in it. Sometimes, however, you may have a good reason to for some other user to own some file, even in your home directory.
You could do it with something like this:
find "~/Music" -type f -exec chmod 644 {} \;
find "~/Music" -type d -exec chmod 755 {} \;
For example, if you’ve copied a bunch of music files from an NTFS drive, this will set the permissions of all directories inside ~/Music (and inside any subdirectories in that directory) to 755 and permissions of all files to 644 (again, in the entire directory tree). However, if you have any files and directories where you want different permissions (for example, executable scripts), those will also get changed. This is unlikely to be the case in a directory like ~/Music, but in some other directory like ~/Programming/Scripts it may be an issue.
And you can fix the 1001 group with:
find "~/Music" -group 1001 -exec chown tadpole:tadpole {} \;
If you run this, there will be no files or directories owned by the 1001 group inside the directory tree starting with ~/Music (again, just an example), they will all be converted to tadpole. This one should be fairly safe to run, even on your entire home directory (but still, there is no warranty).
However, I don’t think this will fix your symlink issue. I still have no idea what caused it. Can you explain the problem in more detail? In what way do programs fail to respect the symlinks?