Gel stains have some poly mixed in but you can put more sealer over
them if you like. If you do two coats of the gel then you probably
don't "Need" a sealer over that. Second coats of gel stain are quite a
bit more useful than a second coat of a typical oil stain. Dark stains
especially look much darker with a second coat.

Yes lap marks can be a problem if it dries before you do the next
section. I like to do all of any given face at one time.I like to use a
stiff brush and really put a lot of gel on the surface, way more than
needed, then wipe it down with a cloth. If the area is just to big,
then do the same to a smaller area but leave a wet edge to start the
next section after wiping most of the first section.

Because you are using Oak, and you want to go dark, you need to be
careful to get the stain down into grain lines. Circular crubbing with
a stiff brush will help.Oak is notorious for haveing little white
streaks of grain after the stain dries, specifically water based stains
with surface tension problems in the little grain valleys. Gel is much
better at filling, but scrub it in to be sure.