Connecting to an IR sensor to a microcontroller module without soldering pins
My first question is whether the electrical connections will work without soldering?


Probably, but not very reliably.


  the USB gets regulated down to 3.3V so I need to use a power supply at 5V. Is there a quick fix for this


Use the USB voltage directly instead of going through the regulator. If necessary, cut the USB cable open, measure the wires, and use the ones with 5V between them. 

Note that if you short the output, the USB output of the USB power supply or computer might get damaged. And of course, if you apply 5V to inputs that expect 3.3V, the inputs may become very unhappy.


  what are these cables called?


Many things. Breadboard wires, jump/jumper wires, Dupont wires, to name a few.