Can terminal cancers go into remission?

Yes. It depends on the type of cancer. "terminal" usually means stage 4 cancer that has spread throughout the body. Cancers can be thought of as "solid" tumors (cancer of the breast, lung, liver, colon, etc.) or "liquid" tumors (leukemias and lymphomas). Solid tumors that are stage 4 may go into remission but almost always come back. Liquid tumors that are stage 4 can often be cured.
Yes. Yes. Remission means "not seen"; however, the cancer may still be present on the molecular (few cells) level and return.