hi
yes you can do overhangs - not sure to what angle but can go less than 45 degrees - see the thing i am printing right now - has a hollow pyramid thing in it.
you can also get the programs to build some plastic to support the overhang if required (called support structure).
yes you can print a box lid. i haven't done it but other do it all the time.
it is called bridging. normally your setting will make the nozzle zoom fast across the gap and the plastic trails behind and goes across.
after a couple of layer doing this is is normal again.
i do not know what distances you can bridge - i'm sure the more experience guys have had competitions to see the max they can go..
good luck
roger
Prusa 'Explorer' (3dStuffMaker), GEN6, J-head Mk III-B, Bowden Extruder, Marlin 1.0.0 RC2, Repitier-Host V0.84 and Slic3r 0.9.8, PLA. Live at Victoria, Australia.