Er dr diag: strained rotator cuff. Can the rc be completely torn if I can't lift my arm up and don't really have much pain? Will see orthopedic dr.

Yes. Yes, the cuff can be torn. This leads to pain and weakness. Pain can be mild too. See ortho doc.
Yes. Rotator cuff initiates the first 10-15 degrees of arm elevation at shoulder.If you can maintain arm elevation after you have passively elevated your arm with the other is one sign of rupture. Nerve injury can also cause the symptoms you are describing.
Potentially. You will need an MRI to define more exactly what is going on, but a good orthopedist can determine a lot on physical exam.