Problem with GFCI at start of circuit with both lights and two receptacles
Lights?
A GFCI can protect lights. You just usually don't need to protect lights. Lights that are installed out-of-reach in the ceiling are normally not required to be protected by GFCI simply because GFCI would not help. GFCI protects against current leaking through a person. If you can't touch the light, no current can flow through you. There are some exceptions: lights above a tub or shower and some outdoor lights, especially if near a pool or other water.
However, there is nothing wrong with GFCI protecting lights. Just keep in mind that:

If your lights &amp; receptacles in a bathroom are on the same circuit and the lights are protected by the same GFCI that protects the receptacles, then if the GFCI trips, the lights will go out. You might be holding a hair dryer or other device that, while at that point no longer an electric shock hazard, might still not be a good situation in the dark.
If your lights use a smart switch that relies on leaking a little current to ground, that could cause nuisance trips of a GFCI.

Line vs. Load
With a regular (non-GFCI) receptacle, you typically will have &quot;incoming&quot; hot/neutral and &quot;outgoing&quot; hot/neutral, and it doesn't matter which wires go to which screws, as long as you get &quot;hot&quot; vs. &quot;neutral&quot; correct.
With a GFCI, it matters. A lot.

Figure out which set of wires is &quot;incoming&quot; - i.e., hot/neutral coming from the circuit breaker. There are a number of ways to do this if the wiring isn't obvious. I would turn off the breaker, disconnect all the wires from the receptacle, cap them for safety, turn on the breaker and check with a non-contact tester.
Connect the &quot;incoming&quot; wires to the LINE side of a GFCI receptacle.
Test the receptacle - it should work fine with normal loads. TEST/RESET should work for testing the GFCI functions, as well as a &quot;GFCI tester&quot;. If you have problems at this point then your wiring is really messed up or you have a bad GFCI receptacle.

Now that you have the LINE side working, connect the remaining hot &amp; neutral wires to the LOAD side of the GFCI. If it trips immediately then you have  ground fault somewhere in the existing LOAD-side wiring (the lights or other receptacles). If it does not trip then use a GFCI tester to test from each of the other receptacles to make sure everything is good.
FYI, the lights on the &quot;GFCI tester&quot; have absolutely nothing to do with GFCI. The tester is really two functions stuck in one convenient package:

&quot;Magic 8-ball&quot; (Harper's term) tester for hot vs. neutral vs. ground connections. Not 100% reliable for diagnosis of a particular problem, but very useful for basic testing.
GFCI tester - drains a small amount of current from hot to ground to test GFCI functionality.