DIYbanter - Concrete removal in basement

Before I head into the basement this weekend, I thought I'd better see
if there was any advice on my two concrete removal projects I have
ahead of me.

The first project is to break up/remove a concrete shower base that is
about 36"l x 32"w x 4"h. I believe previous owners poured this slab
directly over the existing basement floor and I'm not sure if there is
rebar in there or not - haven't seen any signs of it yet but that may
not mean much. I've managed to remove a bit from the outer edges with
a hammer and cement chisel but I've reached a point where I can't seem
to get any more to break off. I was thinking of renting a jackhammer
in hopes the job would go quicker. I'm most concerned about going to
far and start breaking up the basement floor. Would you recommend a
chisel or a point?

The second project is to break up/remove a piece of raised concrete
poured under my stairs. The stairs start in the basement, go up 13
stairs to a landing at the back door and then turn to go up 4 stairs to
the main floor. This piece of concrete is about 60"l x 6"w x 4"h and
appears to be lined up under the one side of the landing. However,
there is no support beam of any type that would indicate this piece of
cement was supposed to be part of a support system. I would like to
remove this piece of cement to make the floor smooth. Should I be
removing this piece of concrete or just build a some sort of raised
floor over it?

Thanks for the suggestions and any tips you have on how to approach
these jobs.

L