Tzekl,
I am not an electrician, nor do I have the NEC Code book yet, so I would immediately defer to TK's responses. Prior to doing any work on the wiring you need to turn the supply breaker OFF. Working on live wires can get you dead or severly injured. Please don't try to prove how easy it is to kill yourself. Of course if you list me as your only benificary, I might reconsider my prior statement. 
Before I start making any suggestions I need to know how you wired all switches and outlets.
I am first concerned about the amperage of the source load line (black) at the panel box. If it is 15 Amp and you are using a 20 amp GFCI, you may have to pull a new 20 amp line from the panel box to the bathroom.
In general, (I believe) you should bring your source power to the light box. You would then run what's called a switch loop to the switch and tie the source to the black of the switch loop. At the switch as well as at the ceiling box you place a small amount of electrical tape around the white insulated wire from the switch. You do this so you know that this particular wire is no longer a return wire, it is a Hot or Load wire. Then you connect the white wire with tape on it to the black wire of the light fixture. And the other end of the marked white line to the other end of the switch.
That gets you your first light working. Now, Is everything supposed to work off of this one power source? If yes, have you tried to reset the GFCI outlet? Also with a meter or a circuit tester, let verify that you actually have power to the GFCI outlet.
Do you understand how a GFCI Outlet works and what it does? There is a very good book called "Wiring Simplified", put out by Black and Decker, which is available at Lowes, Home Depot , Barnes and Noble, Borders. This will explain how to plan your new circuit and how to correctly wire the circuit to meet the NEC Code.
A GFCI outlet uses a small chip in the outlet to induce a signal across the return line.
If the signal remains balanced, every thing works fine. However, if the signal changes, and the amperqage climbs, the outlet opens.
The outlet chip is looking for two conditions:
1) Hot Fault - The source power gets crossconnected to a return or ground line or a short exists.
2) Ground Fault - the signal induced across the neutral or ground wire changes because the amperqage of the neutral iws higher than the amperage on the ground side. The amperage I am speaking about is that of the induced signal by the GFCI's chip, not the circuit's amperage.
Linear Mode
