The questions seem somewhat general, so my first set of information here will be unlikely to tell you what you want…instead it is geared more towards finding out more about what you really want to do.
In general, a Jetson under L4T is no different than any Ubuntu system. If you used L4T R24.2, then this corresponds to Ubuntu 16.04 LTS. If you used an older L4T, then a Jetson would use Ubuntu 14.04 LTS. Most documentation specific to Ubuntu version applies to the Jetson.
Some kernel arguments have an effect on boot behavior, including arguments controlling which runlevel the system boots to. Those arguments are part of the “APPEND” key/value pair to a boot entry in “/boot/extlinux/extlinux.conf” (this APPEND key/value pair is one very long line, don’t let line wrap fool you…keep it as one long line to avoid breaking it).
Should you want the video to stop at text mode instead of graphical mode, some systems allow using kernel parameter “text” to do this. In newer systems, you would add “systemd.unit=multi-user.target” to stop at text mode. To avoid echo of lots of startup messages to console, you would typically add the argument “quiet” to the kernel arguments.
When using graphical mode people often do not realize that X11 is separate from the window manager and login manager. X11 supports a single graphics program, and has no login/user knowledge other than who it runs as. A stock Linux system will run a login manager (e.g., kdm, gdm, xdm) as the argument to X; upon picking a user to login as, X restarts as that user, and instead of naming the login manager as its argument, names a window manager (e.g., unity, KDE, or some GTK desktop window manager). You can replace the argument run by X at start to be your program, and X will run just your program without any window manager or login manager (be sure to set it up to run as your user if you don’t want it to run as root). You could set up the login manager to remain as is, but to only offer some custom program once logged in…you’d avoid the window manager. None of this is specific to a Jetson, the information is the same on any Ubuntu system, and often among different Linux distributions as well (different distributions tend to differ in defaults for X, and not in general setup).
The part which does differ in Jetson is that the driver which X uses is specific to the Jetson hardware. You could not use a different version of Xorg with that driver unless the new version supports the same ABI version.
If you don’t want a monitor attached, but still want the GPU to work, you may want to install a virtual X server matching the Xorg ABI (virtual desktop software does this). GPU software works through the nVidia driver which implies you need the X server to load the driver…else you go back to software rendering and would lose CUDA.
X can have multiple monitors, and each can be configured to be active or inactive. You need a monitor to have proper EDID response if you will use automatic configuration. Without EDID you can still fill in the xorg.conf file by hand, but this is a non-trivial task to convert raw detailed specifications of the monitor into modelines if someone has not already provided this. The topic is not any different under a Jetson with L4T than it is for any other X11 information for any other Linux distributions.