Is a woman considered legally married to her husband, who divorced her for the second time, and her 'iddah period has ended, given that they continue to communicate online and he sees her, without explicitly taking her back? And is it permissible for her to uncover herself in front of him and treat him as a husband?

The enjoyment you two experienced through talking and looking at each other over the internet does not constitute a revocable return [ruj'a], nor does it have the ruling of a private seclusion [khalwa]. If your waiting period [iddah] expires without a revocable return, then you are irrevocably separated from him [ba'inah] and a stranger to him. It is not permissible for you to adorn yourself for him, nor for him to enjoy you. Both of you must adhere to the limits of Islamic law when interacting between a man and a woman who are strangers to each other. If he wishes to return to you, he must perform a new marriage contract.