Regarding your second point... the rule of stalemate is that the player with the move has no legal move. The opponent's possible moves are not considered.
But I think you are asking about a position such as this:
Proverbial "stalemate" ?
Sort:
Yeah I was thinking it had to be sth like that indeed 
Thanks 
It is possible, but probably extremely rare, to have a double stalemate.
| a | b | c | d | e | f | g | h | ||
| 8 |
        |
8 | |||||||
| 7 | 7 | ||||||||
| 6 | 6 | ||||||||
| 5 | 5 | ||||||||
| 4 | 4 | ||||||||
| 3 | 3 | ||||||||
| 2 | 2 | ||||||||
| 1 | 1 | ||||||||
| a | b | c | d | e | f | g | h | ||
Fastest known double stalemate: after 18...dxe3
The fastest known game ending in a double stalemate position was discovered by Enzo Minerva and published in the Italian newspaper l'Unità on 14 August 2007: 1.c4 d5 2.Qb3 Bh3 3.gxh3 f5 4.Qxb7 Kf7 5.Qxa7 Kg6 6.f3 c5 7.Qxe7 Rxa2 8.Kf2 Rxb2 9.Qxg7+ Kh5 10.Qxg8 Rxb1 11.Rxb1 Kh4 12.Qxh8 h5 13.Qh6 Bxh6 14.Rxb8 Be3+ 15.dxe3 Qxb8 16.Kg2 Qf4 17.exf4 d4 18.Be3 dxe3.[20]
Sometimes you hear commentary about a match in any other sport, where really nothing much is going on, they say "It's a stalemate situation".
Do these people actually know what stalemate is? Stalemate ENDS the game. After 20 minutes in a soccer match, what's the use of talking about Stalemate? And, on a more chess-oriented note: would it be possible to construct a position where both sides are in stalemate?