Hi Drashkum,

" The neck seems to be a couple of millimeter broader than neck pocket."

This is normal. The heel of the neck is tapered and will not slip into the neck pocket by sliding it towards the pickup cavities. It needs to be pushed into position from above the body pushing towards the back of the body.

Looking at your pictures, it does look like the high e string side of the neck heel is not flat (it looks like the routing was not finished!) and will need to be sanded!

"Also after fitting the neck into the pocket from the sides, the top of fretboard seems to be a bit higher."

This does look a bit high. Was the neck pushed all the way into the pocket, so that the back of the heel is flush with the base of the pocket? You may find it sits better after sanding the sides!