Why is it leest and not lezen?
Because it is third person singular.
ik lees, jij leest (lees jij), hij/zij/het leest, u leest, wij lezen, jullie lezen, zij lezen.
I'm all over the place with those. Mind, can't expect to grasp everything in a few weeks.
What is different boekt and boeken?
If I have a dutch sentence like that to translate to English I always have to write "is reading"...otherwise it's marked wrong...that's silly...