1. No. Puting a creature into play is not playing it, so neither Standstill nor Throne of Bone will trigger (even if the card were black, which it's not when it's facedown).
2. You can't counter the flip, because it is not an activated ability, which you can tell because it doesn't use the templating "cost: effect," and it is not a triggered ability because it doesn't start with 'when', 'like', or 'as'.
It's a static ability, just like morph, and can't be countered. Furthermore, even if you
could counter it, it has no cost to speak of, and he could just play it again.
Illusionary Mask
Artifact
: Put a creature card with converted mana cost X or less from your hand into play face down as a 0/1 creature. Put X mask counters on that creature. Play this ability only any time you could play a sorcery.
The creature's controller may turn the creature face up any time he or she could play an instant by removing all mask counters from it. This effect ends if the creature is turned face up.
3. Again, yes, because it is not an activated ability, which are always phrased as "cost: effect". Note the colon (':').
