Looking at pic #5, from the reflection of the strings on the pickup cover, the pickup looks too high to me.
As EssentialTension says it's normal practice to set your action and intonation first and then set the pickup height. Try lowering the pickup (both sides/all screws) until it's clearly not interfering with anything (ie. a bit too low). Then do a basic setup - neck relief, saddle height, intonation - to get it playing as you like it. Lastly, adjust the pickup in small increments to get an even output across the strings. Start with the E string side and make sure the pickup is set below the point at which the string hits the pole pieces when playing normally. Then adjust the other screws to balance output with the E string.
Remember that any recommended settings you find for pickup height/string clearance (eg. Fender setup guide says 2.8mm on E side and 2mm on G side) are measured from the bottom of the string to the top of the pole piece [u]while fretting the string at the last fret[/u]. The unfretted string clearance is much greater.
Pickups don't necessarily need to be maxed as close to the string as possible to get good tone, winding them down a bit can open up the tone and give a more even string balance.