How many LED's on Pin 13 that already powers the on-board Green L-LED?

"Does this mean I cannot connect 2 normal LED's on Pin 13?"
Better answer is Maybe.
Recent Uno's have a buffer (LM358) on D13 that drives the onboard LED. Older Unos have a 1K resistor to the LED, which consumes ~3mA of current when driving High.
Both early and later have recommended Absolute Max of 40mA both high & low. However, high voltage drops down as current exceeds 20mA, and low voltage rises up as current exceeds 20mA.
There is also a limit on how much current a port will support, and an overall limit on how much current the Vcc/Avcc & Gnd pins can support. (200mA/pin) See Section 29 of the datasheet, excerpted below.
Depending on Vf of your LEDs, you might be able to run them at 20mA by putting both in series with a single resistor.

ATmega328P:
DC Current per I/O Pin ................................................ 40.0mA
DC Current VCC and GND Pins................................. 200.0mA

  1. Although each I/O port can source more than the test conditions (20mA at VCC = 5V, 10mA at VCC = 3V) under steady state
    conditions (non-transient), the following must be observed:
    1] The sum of all IOH, for ports C0 - C5, D0- D4, ADC7, RESET should not exceed 150mA.
    2] The sum of all IOH, for ports B0 - B5, D5 - D7, ADC6, XTAL1, XTAL2 should not exceed 150mA.
    If IIOH exceeds the test condition, VOH may exceed the related specification. Pins are not guaranteed to source current greater than the listed test condition.

  2. Although each I/O port can sink more than the test conditions (20 mA at VCC = 5V, 10 mA at VCC = 3V) under steady state
    conditions (non-transient), the following must be observed:
    1] The sum of all IOL, for ports C0 - C5, ADC7, ADC6 should not exceed 100 mA.
    2] The sum of all IOL, for ports B0 - B5, D5 - D7, XTAL1, XTAL2 should not exceed 100 mA.
    3] The sum of all IOL, for ports D0 - D4, RESET should not exceed 100 mA.
    If IOL exceeds the test condition, VOL may exceed the related specification. Pins are not guaranteed to sink current greater than the listed test condition.