Live wire , neutral wire confusion
First of all, whatever it was that you read, was (partially) wrong.  During half of the AC cycle, it flows one way, then during the other half, it flows the other way.  So your #1 is correct.

For #2, the bulb is really more of a heater that simply gets so hot that it glows.  (assuming incandescent; CFL's and LED's are much more complicated)  Temperature takes a relatively long time to change in most cases, so it easily rides through the AC zero-crossings.  Keep in mind that these zero-crossings happen 120x per second for 60Hz line frequency, so even traditional fluorescent bulbs that do turn off at zero are difficult to see doing that without something moving to complete the strobe effect.