I can't help you with the registration, so rally points it is.
In the lower left corner of the main screen, just above where it says what you're researching, there is a circle and arrow icon. Clicking on this will turn your cursor into that, then clicking on your selected location on the map will create your waypoint. You will get a pop up that gives you a choice between normal (ship just stops when it gets there), fleet (ships form fleets as they arrive as your logistics ability allows) and attack (sets your ships to auto attack on arrival). You also get an opportunity to rename the rally point, to name it something more descriptive than its location.
Once you have a rally point or two made, "t" will bring up the list of available rally points you can send the ship to - home and none are the only options you're getting because you don't have any others made. You can set a planet to send new construction to a rally point by either using "t" with the planet selected, or using the rally point icon on the planet image in the bottom center window of your screen when that planet is selected. I don't know what "x" is supposed to do, so I can't help you there.