Does it learn from me?

Weights, memory and training.

Fixed after training

A deployed model's weights do not change as you talk to it. Memory features store text and reinsert it as context, which looks similar and is not the same.

Your conversations may be used to train future versions, depending on the product.
Check the terms if you are pasting anything sensitive.

The knowledge cutoff

Models know nothing after their training data ends unless it is supplied. Answers about recent events without a retrieval step should be treated as guesses.