It could be a get me’usa, and that is a situation that must be avoided, to avoid mamzerim. Mamzerut is extremely serious, as it is a status that can never be undone.
This isn’t the place to play the gam “my rabbi vs. your rabbi.” But, I do view Rabbi Tucker as a gaon. His knowledge of halakha is astounding in its breadth and depth. Many of his shiurim are accessible, and I, for one, think it is absolutely amazing that people who are Modern Orthodox and from all other denominations are coming together to learn Gemara be iyun. Thanks to Hadar and Pardes, people raised Reform and secular with no yiddishkeit are now davening, keeping kosher, and learning Gemara with Rashi, Tosafot, and other Rishonim.
Men and women learn Gemara at Hadar. The Rav allowed mixed limudei kodesh at Maimonides School, and many other respected Modern Orthodox high schools also have mixed limudei kodesh. I cannot comment on Hadar’s davening, which I neevr attended, and wouldn’t attend.