If I select a random star from the screen, I can find information about it (by pressing "I" key), but that information does not include what galaxy the star is in. How can I find that?
What? Do you mean the star browser? Because if you do, then the star you selected will be in the radius that the star browser says, you can change the size of the radius by typing it in on the top left of the tab. If you mean that you just selected a star just by clicking on it, then that star will be in the galaxy your in because spaceengine only renders 100,000 stars at a time and every galaxy has more than 100,000 stars in it, so if you click on a star, then you are clicking on a star that is in the galaxy your in. To find the galaxy your in, just zoom out and click on the center of the thing that looks like well, a galaxy. Sorry if I misunderstood your question, but that's what seems to be what your asking. (PS) the "I" key brings up the "wiki" feature so it pretty much only gives you the information for THAT object.
I am named after a work in progress...