Hmmm... According to Basement Rules, at
http://www.usatt.org/rules/basementRules.html :
"7.2 The ball must bounce once on the server's side of the table and only once on your opponent's. If it bounces twice on your opponent's side, he's awarded the point.
7.2.1 The ball must cross the end line and must not cross the edge lines on the service."
So, for basement ping-pong, no - to both. (see also
http://tabletennis.about.com/.../importantrules_2.htm )
See some of the various (USA) Rules, here:
http://www.usatt.org/major/rules.shtml and here:
http://www.pongworld.com/more/rules.php and here:
http://tabletennis.about.com/.../importantrules.htm