Grommet does fit in the spacer we do it all the time. Put the spacer on the table and use your thumb to push it in, they do fit. Sometimes I find it easier to put the spacer in the back of the lure after inserting the thru wire, then using the thru wire as a guide to hold the grommet in place you can push against a table or hard surface.
The spacer can be tight in the back especially if you have paint or finish in that area. You can make it slightly larger if need be but those are all done with the same drill bit as many other kits also so should have normal size hole.
No grommets needed in harder woods. If you feel it needs one as some people do then by all means add one but I've never seen a fish stop and look at a lure and decline to eat it because it was missing the grommet