That is the correct levelshifter you linked to. Also note you need the 100nF (.1uF) Ceramic bypass capacitor that is pictured close to the level shifter. -Not sure if that was the capacitor you said you would add, but that one is needed. If you were talking about the 470uF Electrolytic one by the Esp, that one is a good idea for any power dips but is not an absolute needed item.
If you are going to solder the Esp to a prototype board I would use pin header strips, so that if you ever need to remove the Esp it is as simple as unplugging it.
I’m in the USA so navigating that site you are looking to buy from is kinda hard, but I’m talking about these things soldered to the prototype board and the Esp’s pins plugging into them: Pin header kit for Feather, 12-pin and 16-pin socket connectors - buy at BerryBase
I am not sure what you are wanting the screw terminals for when referring to “24v”. Your prior pic shows you have a 5v 30a power supply 
As for using those screw terminals for the data connections and power to the Esp, they would work fine. *I would not use them for power to your LEDs unless you are sure you will be under whatever their current (amps) rating is.
I made some comments in this other topic that may or may not be of help to you, feel free to have a look Roccomendations for Narrower ESP32 Board - #4 by Jinx