What body parts can you train at the gym if you have cubital tunnel syndrome or ulner nerve entrapment in general specifically at the elbow?

Avoid flexion : There are no known exercises that are known to help cubital tunnel syndrome; which, as you said is an entrapment syndrome of the ulnar nerve at the elbow. Flexion and direct pressure can aggravate it, so avoiding flexion of the elbow can help in mild cases. Even to the point we used to have patients use a knee pad and put it in the elbow reversed to keep the elbow straight.