Android not detecting USB though it is connected
To answer the last question first, yes it is save to tether with debugging mode on.

I'm not sure about the answer to the first question, because i'm not well known with cyanogenmod. If you were a normal android user i'd suggest looking if the MTP or PTP settings are set well. You can find these under Settings &gt; Storage &gt; USB computer connection

Hope this helps. I found this useful on my Nexus 4 using android 4 and android 5