It is basically connected to USB, and can provide up to 500mA. Again, and someone has mentioned it before, when you measure current, you are measuring what your circuit is using not what it can provide.
You guess, but not correctly.
The circuit should work, so hence my suggestion. Disconnect all, and re-connect all.
How about you post a picture of your setup You wouldn't be the first to miss a connection somewhere. I have done that more times than i can remember. Just the other day i put a Pro-Micro on the breadboard, and it didn't work, turned out there was still a jumper connecting 2 pin (and 1 was RST and the GND)
Since you have already done that, it is quite possible your ESP-01 is already fried. (actually quite a likely scenario)