This actually requires a fair amount of skill, and your question is really
simplistic. Have you ever even finished a slab before? I would suggest
hiring this out - even if you think you can't afford it.

You are quite right to say that. Now, after having tried and failed to
level the floor myself (two months ago), I would think that I should
have forgot about the idea of leveling the floor (for putting tiles)
and live with the uneven floor and bare concrete floor. But now I am
at the point of no return. I will have to get it done.

Pro finishers get a much better deal on concrete. When you also factor
in your time and poor results, I think you will find a pro to be a
bargain.

If I could started this over with, I would be better off hiring this
out. But I am now so close to the finish-line. I really want to get it
done.

Various extenders are available - but they only extend the set by, at most,
90 minutes.

90 minutes is more than enough for me. This means using extender is a
good idea for me. Thanks.

If your old floor is sinking - you may be heading down the wrong road
anyway.

Luckily, the floor is not sinking. The concrete floor was not leveled
properly when the house was constructed back in 1950's. I have a
feeling that the basement was not meant to be finished when the house
was constructed. Therefore, making it level was never a requirement
back then.

Jay Chan