I would like to cut this mesh into two parts where the Plane is located and have the resulting openings filled. I've tried the knife tool and bisect but I can't figure out how to execute either of them. I did see a similar question here maybe a year ago but I can't find it. Thanks in advance!
Previous answers will work, but two other options need to be given. 1. Booltool addon - add a Solidify modifier to the Plane object, and then shift-select your target object and choose Difference bool brush. 2. With all the faces selected, you can use Shift-K to draw the knife tool through the mesh in edit mode so that it creates a cut even through odd ngons. After, you can select this new loop and use V to rip and then select one side and separate like explained before.
Yeah you can press Crtl-R in Edit mode and select the loop direction you want and then the location of the knife cut. This will create a straight line made of edges around the the mesh. You can then select one half and press P, then separate by selected.