A couple of additional points to consider.
(1) The higher grit sandpaper you use, the less stain soaks in. That's
because there's less exposed grain for the stain to seep into. I
usually sand raw wood only to 180 - except the end grain (if that's
going to show) which I sand to 320. If you find that the stained color
is close but not deep enough, you can always try applying a second coat
of stain. Realize that the second coat will soak up less than the
first coat too.
(2) I also don't sand between the stain and first coat. Too much risk
that I'll sand through the stain someplace. If you want to sand here
(because the stain really raised the grain), go easy using with a 320
I completely agree about using 320 between each coat of seal and go
with 3 coats of seal. You'll end up with a really smooth surface -
almost certainly smoother than your current cabinets! Doing anything
after the final coat is up to your judgement. If the final coat feels
smooth to the bare hand, don't worry about it - especially for cabinet
type of work.
My major concern would be ending up with something that looks right
color wise but is finished much nicer than the rest of your cabinets -
which might make it stand out. If that's the case and you want to try
again, sand back down to the raw wood stopping at 150 and only apply 2
coats of seal - that's probably about as much as the original cabinets