Starter, bad alternator, or worse?

Hi, I’ll be detailed.

I have a 2003 Ford Focus SE with 127k
miles on it, yesterday I was driving a friend
home and the battery light turned on for a
second and then turned off. When I was
driving myself home later, at about 40 mph
there was this jolt as if I ran over
something, my abs and handbrake lights
went on and then off, engine light, oil light,
battery light all went on and car stalled. All
lights, radio, everything remained on, but
the car stalled. it started in a second just
fine after i panicked for twenty seconds.
The next morning it didn’t start. when i
would try it would click but no crank no
start. we took the battery to get recharged
and they told us it was an okay battery and
when we got back it cranked but didn’t
start. twice. this was some progress, so we
tried jumping the battery through a
portable charger, it didn’t work at first but
in a second the car started again. We want
to get the alternator checked out, but what
other problems could this possibly be?

In addition, when we started the car and
started revving up the engine the lights in
the car started dimming (which is why we
assume it’s the alternator). when the car
started there were no warning signs or
anything, oil light, battery and engine light
all turned off on second start which was
successfu.
HOWEVER when i first started the car the
oil light would slightly flicker but not come
on when i would do some things, and then
i realized that when i kinda shook the car
by sitting down the light flickered and went
on? coincidence? i think not!
how bad could this be? the engine seems
to be doing fine