I dissagree because the OP's 5V load is only 100 mA @12V. (P=I*V)(The devices he plans to power wth the 5V Vcc pin do not exceed 266mA@5V (100mA@12V)
Don't power the Arduino with anything >5V for a long term project. That RAW input is for prototyping/testing only, and even then not the greatest of ideas.So what you need is a 2-3A 12V supply (some derating here never hurts, a 4-5A supply will do just fine as well), plus a 12V-5V converter for your 5V parts including the Arduino, a buck converter will do great here. Of course you power the Arduino over its 5V pin (that's what it really is for), and the rest of the 5V stuff directly to your 5V supply.Remember to connect grounds. Consider using a MOSFET instead of a relay to switch that solenoid.
The OP isn't planning to overload the 5V.All he wants to do is power his solenoid and the uno and few other things from a single12V power supply .
An Uno will eventually overheat/reboot if you draw more than 150mA total from any pin.Make sure your supply is regulated. Unregulated ones could have >17volt unloaded, which will fry the Uno.12volt is already borderline for an Uno/Mega, and smaller boards will eventually release the magic smoke at that volatge.Common 5volt relays draw about 75mA coil current, plus 2mA I/O pin current.A membrane keypad runs on fumes, unless it has got some LED illumination inside.160mA sounds a lot for an LCD (backlight). The LCD itself (no backlight) could draw 20mA (educated guess).Don't forget the back-emf diode across the solenoid, even if you use a relay to switch the coil.Otherwise you will be rewarded with random resets of the Uno.Leo..
That buck converter will not create 2.5A just like that. Many are not even capable of such output currents. That you even write it like this tells me you still don't understand how current works.Also you could of course simply have the buck converter produce 5V and not need the on board regulator at all...
A 1.5A supply is anyway pretty minimal for a 1.2A solenoid plus the rest.
Try with just switching on and off the LCD backlight. You probably also see that 0.05A difference. Or at least it should be about 0.04A. The display itself needs only very little current.
Don't power the Arduino with anything >5V for a long term project
Define "long term". I have a UNO project with 12V in to the barrel connector that's been running for the better part of a year.