With regards to #2 It is not common courtesy to check it down, it is collusion (which is against the rules). However, it is a sort of unspoken rule of thumb to check it down to increase the chances of busting the all in short stack. If one of you hits a big hand, you should bet, the other player gets out of the way.

As for #1 The big stack sitting out, this happens, just play as normal but be more aggressive when he is posting a BB.