1. Is it permitted to pour coffee from a French Press coffee maker on shabbos?
2. Also can I use it to prepare cold brew on shabbos itself (allow coffee grinds to soak for a long period of time)
1. You should not push the strainer all the way down to the bottom and then you may pour it on Shabbos, as long as you leave liquid on the bottom.
2. Yes, but be careful not to push down the handle all the way, as that would be borer.
Rabbi Shay Tahan