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Hey I wanted to ask if the the distance between the strings and the pickups is fine.
It looks like the strings is closer to one pickup from the other one.

that looks extreme , but its normal for the pick ups not to be the same height ..... that's how you balance the sound between the two pick ups ....... does the neck pup sound louder than the bridge ??...... if so adjust the height to balance the loudness between both
I do hear huge volume difference between the pickups Should I raise the pickup or lower the strings?
You want the bridge pickup closer to the strings than the neck pickup.
Lowering the strings would affect your action, so if you don't want to do that just adjust the pickups.

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That neck pup looks too high to me, but its hard to tell from just one pic.

What you should do is adjust the strings to whatever height feels best to you, then you adjust the pickups where they are about as close as they can be without killing sustain. After that you will have to adjust the pickups so that they have equal output, usually by lowering whichever one is louder.
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i hate to say this, but trial and error. every pickup is different, different strings are even different. its not hard to move it up and down as you mess around and play.

the biggest thing is to be able to fret at the last fret and not have the pickup intervene with the natural string vibration movement.

mess around and see how you like it and keep it there. all you need is screwdriver and a few minutes.