Can I plug an electric guitar into a bass amplifier without damage to the amp or the instrument.?

Yes you can, I know several very excellent guitar players who use a Fender Bassman amp on their gigs and they sound fantastic without any effect pedals as well, now on the other hand playing a Bass guitar in a guitar amp can blow the speaker at high volume.

yes

Yeah it's fine. You'll just get a deeper sound with a bass amp. Queens of the Stone Age use that technique quite a bit, and its the only way to play "No One Knows" without sounding flat.

Why not take it up a level? Plug your guitar into a signal splitter, run one of the signal splitter's outputs to your lead amp, the other output to a delay and then on to the bass amp. Don't OD on the delay, a little goes a long way with this set up. This works really well if playing solo or with a small group. You get a fatter, fuller sound.