"We have 3 landing pages going to 1 sales page. Does this sales page need 1 conversion pixel or 3?
You need one conversion pixel for every sale (thank you) pages. In this case you just need one conversion pixel.
So you should create and install only one conversion code (pixel) for every sales page or for every kind of conversion you need to track.
For example in ClickMeter we have 2 conversion pixel in the same thank you page. One is to track how many signed up for free and the other is to track who upgraded to a paid subscription.