A question about space-time diagram

"Simultaneously" is a comparison which requires two events and one reference frame. If event $A$ is simultaneous with event $B$ according to reference frame $S$ then that means that the time coordinate of $A$ is the same as the time coordinate of $B$ both according to $S$.

In principle, you could set $B=A$ and then have one event and one frame, but there is no way to express the concept of simultaneity for one event and two reference frames. It just doesn't fit.

In the diagram event $E$ is simultaneous with any event on the white dotted line $t_0$ according to the unprimed reference frame and event $E$ is simultaneous with any event on the red dotted line $t'_0$ according to the primed reference frame. That is really all that can be said.

In the light diagram there is only one point such that an event that happens in that point happens in the "present" moment for both the frames (in the sense that I interpreted from your question), and it's the origin. And this means that if we define as the event $A$ the one in which "one hand of one observer from the blue frame touches one hand of one observer of the red one", then a statement of the type "events $A$ and $B$ happened simultaneously" can be true only if both their coordinates happen in the origin. Indeed, if we consider events $A$ and $B$ simultaneous for the blue frame, it means that they have to be aligned horizontally in the graphic, and because of to be simultaneous also for the red frame they should be aligned not horizontally but in a way parallel to the red $x$ axis, we can conclude that it's not possible that they happen simultaneously both in the red and in the blue axis, unless they stay both in the same point, and it can be only the origin because event $A$ has to be in the $t=0$ for both the frames.