She could do this after the lesson ends. She could have done that after the lesson needed. Keep the tenses the same.

The second is correct but it is expressing possibility in the future, or a conditional idea. The meaning is that it would be possible for her to do this after the lessons ends (or has ended). The first is not correct. 'The lesson ended' places the event in the past. You can say 'She could HAVE done this after the lesson ended'. This means that it was a possibility in the past (but she did not actually do it).

Both can be correct, but they refer to different times. “She could do this after the lesson ended.” Past context. You’re talking about something possible after a past lesson. “She could do this after the lesson ends.” Future or general context. You mean after a lesson (in general) or the next one finishes. About your question: Yes, “could” can be used with the present simple. “Could” is a modal verb, and the verb after it stays in the base form, while time is shown by context. Examples: “She could go after the lesson ends.” “We could talk when he arrives.”

Correct: “She could do this after the lesson ends” Unclear and unnatural, but "grammatically correct" : “She could do this after the lesson ended”

It really depends what you have in mind. Without context, there are many possible meanings and tenses. In fact, like many modal verbs, 'could' has several meanings in general. She could do this after the lesson ended. = imagining hypothetical (similar to 2nd conditional) OR reported speech with back-shifting to describe what she said she could do ('could' is the conditional form of 'can' *and/or* the past form of 'can') She can do this after the lesson ends = simple and realistic (similar to 1st conditional) She could do this after the lesson ends = Also fine... it's relatively common to add could/would to show politeness, not for grammatical reasons I would also recommend thinking about another version: She can do this after the lesson has ended. Present perfect is good for talking about things that are done or not done, without mentioning a specific time. Why not future perfect (after it will have ended) or future simple (after it will end)? Because we usually don't use 'will' with certain time words like: if, when, before, after, until, etc.