hook up the monitor to the external monitor port.
Install the mouse and not the keyboard .
Start the system. Do not go into the BIOS (set up) and disable any of the laptop hardware. The other added mouse will auto detect and become usable.
Now on the laptop keyboard you need to use the FN key and the monitor switch key (usually located on the upper left of the keyboard. this will switch your graphics to use the external monitor. Once done this should promote the external monitor to be primary monitor. to test shut down the system and restart it. If the external monitor starts then you are fine. If it reverts back to the laptop then you must open the graphics properties and set it to use the external monitor. When you have the external monitor configured to be default. then you need to go to control panel and power options and locate the lid closure options and change it to do nothing when the lid is closed.
I would also turn off hybernate while in the power options category.
Once that is all configured and you have verified that it all starts when rebooted then I would add the other keyboard and reboot. That should get you to doing what it is that you want to do.
There are a few things that you should watch out for.
1) the power pack that comes with your computer is not designed to stay on or plugged in continuously. So it is best to shut the system down and unplug the power adapter or it will overheat and burn out fairly quick.
2) the laptop in a closed position will be blocking some intake venting for cooling purposes. Keep it elevated so as to continue as much cool air flow as possible or you might start experiencing some overheating issues.
You might look into buying a docking station for the laptop to run it as a desktop on a more continuous basis. The docking station will give you a new always on power outlet and also use some aditional cooling fans to keep it cooler along with other options as more USB ports. Buy an Home Office Essentials Bundle (901805) from HP® Official Store