Did Leave or Did Left?

He did leave - the structure "did + bare infinitive" makes past tense. e.g. I did leave, you did leave, he did leave, we did leave, you (pl) did leave, they did leave. For example: I did see.

Did someone leave or left?

Has they left is incorrect, Has he/she left is the right response. Did they left is incorrect, Did they leave is the right response. The rule is to use plural object with singular subject and vice versa.

Did she leave or left?

The preferred form is Has she left yet? In American English it's quite common to hear Did she leave yet? as well. There is no significant difference in meaning.