Yes. This resistor is made of an ohmic conductor. If we used a light bulb, for example, this would not work, because it would heat up considerably and its resistance would increase. However, in this case I am using a resistor that has the same resistance for all of the currents measured.

Start at the negative terminal of the battery/power supply. Connect your first wire. Follow your circuit diagram and connect each component, one by one until you get all the way round to the positive terminal. Then connect all of the things that need to be in parallel. If the circuit doesn't work, try wiggling each connection to find where the loose one is. If it still doesn't work, try switching out each component, one by one. It can be a bit annoying/frustrating.

I can see where you are coming from, but with these currents, measured over this length of time, the impact is small, as the results show.

Current is negligible