OK, so maybe not as different as it appeared in the photos, but still enough to make it awkward.

No, you won't need to trim the end off the 22 fret neck; the overhang is normal on those. Though the ends are normally rounded over a bit, rather than left perfectly straight edged as yours is at the moment. You could trim it back a bit if you wanted to, but you'd be best to leave at lest 5mm of wood on the body side of the 22nd fret to give the fret and its slot some support.

Whilst the neck pocket should in theory be slightly wedge shaped to match the neck shape, because the treble side of the pocket is mainly open, I've never needed to slot a neck in from the top (though I dare say that you might need to on the odd guitar if it's a very tight fit.

Don't forget that the neck will also be a bit wider by the time you've put some finish on it. Whilst it's normal not to finish the inside of the pocket, finishing the neck is normal. So you don't want a very tight fit for the neck before you add any finish, or you simply won't get it in there when you do. How much extra width will depend on just what finish you use and how much of it you apply. But it could be anywhere from 0.1mm to almost 1mm in total.

Whilst you don't want big gaps round the sides of the neck, the main areas of concern are the heel bottom to pocket bottom contact and the neck end to pocket end contact. The neck screws will hold the neck in place regardless, but you do get a bit more sustain if the neck also sits snugly against the end of the pocket.