How could I print a large sphere-like object?
A sphere can be put together quarters easily, but those need support in the center. However, there is a slightly different cut is more economic:


Cut a top and bottom "plate" off, print them separately, the lower one "upside down"
Cut the remaining piece into quarters


For more equal printing, maybe even cut them along the equator too and print the lower half "upside down"





This way, the support material can be reduced to a minimum - only the top and bottom will need any support, and it is easily accessible to smooth it away.

If the walls would be something like one millimeter thick, any good glue should work. If you want to reduce the visible seam, you might bevel the faces, so that the wall has a little gap on the inner wall. As most glues shrink as they harden, it will flatten into the "gap", evening out the internal face.