I think a small laser level would help me a lot, but I'm not sure. Let's
say
that I have a curved surface, a rough hemisphere for example. I'd like to
cut the hemisphere in half, or at least slice it so the cut edge is
straight
and can be fitted onto a flat surface. Could a laser level lay a straight
line onto the curved surface, so I could mark it for cutting?

Absolutely! Just make certain the cut you take is flat; that is to say,
parallel to the horizon or perpendicular to the vertical. If the hemisphere
is not perfect, you may wish to position it in such a way as to include the
most pleasing parts of it. Visualize an orange with a small rotten spot.
You'd want to turn it so that the laser illumninated another portion in
order to leave out the bad spot. In other words, you position the subject
(or the laser) in such a way that the area of interest is illuminated.

Bob Swinney