Some questions regarding a schmitt-trigger design
Here are your answers:

1) The resistors R7 and R8 only influence the current through the LED. Changing R1 to set the hysteresis is correct and works, as you mentioned.

2) In my opinion R2 works with C1 as filter to prevent U4 from noise on the supply lines.

3) Typically you use a combination of caps, for example 4.7uF in parallel with 100nF. In your case 100nF should be sufficient or just added to the existing cap. However you should not worry to much about that. This is no high speed or high power circuit.

4) The surge protection must be placed before the caps, because caps suffer from over voltage. Thus the position in the schematic is correct.

5) A cap across R1 can prevent the circuit from oscillation. Try to add 22pF. However this not necessary. Just have a try in your simulation ;)

That's it.