Confused with diodes and conventional vs real current flow
Look, you are just going to have to learn to deal with Ben Franklin's mistake (see hackastical's xkcd cartoon). Most of us have been there in our early days. pipe's comment is spot on. If you're doing solid state physics and talking about n-type semiconductors, then you need to think about electron flow. If you're building an LED circuit, forget electron flow and go with current. Current is produced (in conductors) by electrons, true enough, but electrons flow in the opposite direction as current. At some point you'll understand that it's just a convention, and has no deeper significance, and you can get on with your life.

Now. Your LED issue arises from your forgetting Kirchoff's Voltage and Current Laws: the sum of voltages around a loop is zero, and every connection point has zero net current. So, with 0.6 volts across the two LEDs, each LED must have at most 0.6 volts across it (KVL), and will in practice have less, with the two summing to 0.6. So the 
0.7 volt LED has zero current through it, which means the 0.4 will too (KCL), and with no current through either LED, neither will light up.

And yes, this means that the actual distribution of voltages across the two LEDs is undefined. When you make a more reasonable (realistic) model of the LEDs, leakage effects will allow a more reasonable voltage distribution. But the voltage across the 0.7 volt LED will not reach 0.7 volts and the LED will not have much light output. Depending on the exact materials used, it's possible that the 0.4 volt LED will light up slightly.