Has anybody installed tools service packs without the application service packs? I was told the tools service packs now have dependencies with the application service packs. This wasn't the case before, for example, we have tools 12 installed but only 9 application installed.

There are no dependencies defined in PMC from tools services packs to application service packs. The only exception is SP8, for which application SP6 is a pre-requisite. The reason for that is that upto SP6 tools were included in the application service pack. (SP7 didn't contain tools fixes.)
Of course there can be a note somewhere in the installation guides or in the knowledge base about the compatibility. I did not check that.