I have cancer, can this cause encephalitis?

No. Encephalitis is an infection of the brain. Cancer and the chemotherapy may lower the immune system and increase risk of infection. This is not a direct cause for encephalitis, but just increases the risk. Cancer may spread and go to the brain and produce an inflammatory state similar to encephalitis. Remote effects of cancer can cause strange brain behavior "limbic encephalitis".
No. Encephalitis is an inflammation of the brain and would not normally be associated with cancer. However if cancer spreads the brain, one might develop encephalopathy which can present with confusion, worsening memory, personality changes, etc.