1. CTS is done before nanoRoute, but all the steps up until nanoRoute use trialRoute to do some "unofficial" routing.
2. The opt should not be touching clock nets. The clocks are probably not defined properly in the SDC (constraints).
3. is the pad the root of the clock? If so, then yes you can specify that in the .ctstch. However, you probably want to specify the PAD of the IO cell, so that you get the timing through the IO cell as part of the clock tree.
4. CTS needs to be done before nanoroute - usually the clocks are detail routed at the CTS step when all the routing resource is available.