Floor to bottom of joist is 9'. How do I test whether the floor is
perfectly level? There's a bilco door from the basement to the
outside. I'll try to integrate that into the bedroom floor plan
instead of putting in a larger window.

9-ft should be enough. 8-ft for living space should be enough to meet
the code (please check your local building code). Then you will have
1-ft left for the flooring and the drop ceiling. A drop ceiling with
2'x2' square grid should only need very little vertical space
(something like 6" or less) for moving a ceiling tile in place. Then
you will have as much as 6" for leveling the floor and for the
flooring. 6" sounds a lot. But some methods of leveling the floor may
require you to have a raised floor, and 6" may or may not be enough.

There are probably many ways to check the floor to see if it is level.
The way that I suggest is to use a water-tube-level or a laser-level to
draw a level line around your basement wall. And then transfer that
level line down close to the floor level -- such as 1" above the floor.
Now, you have a solid level line marked on the wall 1" above the
floor. Then you need two persons to do the following:
o Each holds one end of a string.
o Move to a corner of the basement.
o One person holds the string against one side of the wall right
at the level line that you have drawn; another person holds
the string against another side of the wall also at the level line.
o One person moves the string along the level line. This causes
the string to sweep across the floor. The other person observes
the distance between the string and the floor. If the floor is
truely level, the distance should remain the same (such as 1"
in this example). If not, the other person should mark down the
high spot on the floor. The purposes of this sweep are to find out
if the floor is truely level, and to find the highest spot on the
basement floor.
o If the floor is not level, and you have found the highest spot of
the floor, you need to re-draw the level line in a way that the
new level is barely above the highest spot of the floor. The new
level line may be above or below the existing level line; this is
OK.
o Sweep the floor one more time. This time you follow the newly
re-drawn level line. You need to mark down not only the high
spots, but also the low spots, and you need to measure how
deep the low spots are from the level line.
o Now, you have the numbers of all the low spots ready. Draw
the layout of your basement on a piece of paper and put the
numbers on it.
o Examine the numbers to see how bad the situation is. If the
floor is basically level with a small number of sunken areas,
you may decide to level the floor yourself. If the floor is
totally
unlevel, you may decide to hire a pro to level the floor for you,
or you may decide to drop this project all together. If the floor
is tilting to one side significantly, you may need to hire a pro
to see if the foundation of your house is in trouble or not.

I have no comment on how to integrate the basement exterior door with
your floor plan. But if you decide to place the exterior door inside
the bedroom, you may want to make sure that the interior door of the
bedroom is large enough for you to move applicants from outdoor to the
other area of the basement via the bedroom.

Hope your project will be fine.

Jay Chan