Issues with connecting a slideswitch to change between automatic and manual mode for a fan

This is not reading the position of the switch, you need something like:

if (digitalRead(switchA) == HIGH)

similarly:

else if(switchA == LOW)

Needs changing in a similar manner.

Here you are checking whether "switchA" is equal to zero (which is what LOW means), but it can never be, because it is a pin number (which you have set to be 6):

int switchA = 6;