>Ok, but the sewage pipe would be higher than the drains, so a sewage pump is still needed, right?

Probably not. Unless you live in a REALLY strange place, or perhaps have a septic tank system rather than "town sewer connection", then the septic pipe is probably below floor level somewhere in your basement. So the idea would be to slope a drain pipe (under the floor) from the new bathroom to connect to that. 1/4" per foot slope; no more, no less.

But definitely get a plumber. At least to look at it and tell you what to do, and where to do it (videotape is your Friend). Or if cheap enough, to do it all for you.

Cheers