Is it possible to connect them all to a single GPIO port and using 1 resistor?
Yes, but without additional hardware, when one is lit, they will all be lit. Which is the same thing as saying, "When the GPIO is ON, it is ON, and when it is OFF, it is OFF."
Charlieplexing is interesting, but strikes me personally as an esoteric solution looking for a problem :) But rest assured that Charlieplexing is incapable of violating the laws of physics, and there will always be a non-zero potential difference between pins before current will flow & an LED is lit. There is no GND identified in the schematics because the voltages at X1 and X2 are reversed to realize the Charlieplexer. AFAIK, this is not possible with RPi GPIO pins, and even if it were, it's still 2 or more GPIOs.
Your objective of
Connecting LEDs with least pins and wiring may be more practically reached with an external hardware component similar to the ADG2188 - an 8 channel analog switch matrix with an i2c interface. Or, better still, per @joan's comment, get a PCA9685 - 16-channel LED controller that also has an i2c interface. However, the i2c interface still requires 2 GPIO pins.