I have enchanted my opponents commander with Song of the Dryads. He cast Shimmer and when it resolves, he chooses forests. Does SOTD go away when that forest phases out?
No, Song will phase in/out with the forest/commander.
702.25f When a permanent phases out, any Auras, Equipment, or Fortifications attached to that
permanent phase out at the same time. This alternate way of phasing out is known as phasing
out “indirectly.” An Aura, Equipment, or Fortification that phased out indirectly won’t phase in
by itself, but instead phases in along with the permanent it’s attached to.
702.25h An Aura, Equipment, or Fortification that phased out directly will phase in attached to the
object or player it was attached to when it phased out, if that object is still in the same zone or
that player is still in the game. If not, that Aura, Equipment, or Fortification phases in
unattached. State-based actions apply as appropriate. (See rules 704.5m and 704.5n.)
When an enchanted permanent phases out, its Auras also phase out with it, and will return when the permanent phase in, still attached to it. This is called "phasing out indirectly".
702.25f. When a permanent phases out, any Auras, Equipment, or Fortifications attached to that permanent phase out at the same time. This alternate way of phasing out is known as phasing out "indirectly." An Aura, Equipment, or Fortification that phased out indirectly won't phase in by itself, but instead phases in along with the permanent it's attached to.
Shimmer
I have enchanted my opponents commander with Song of the Dryads. He cast Shimmer and when it resolves, he chooses forests. Does SOTD go away when that forest phases out?
When an enchanted permanent phases out, its Auras also phase out with it, and will return when the permanent phase in, still attached to it. This is called "phasing out indirectly".
702.25f. When a permanent phases out, any Auras, Equipment, or Fortifications attached to that permanent phase out at the same time. This alternate way of phasing out is known as phasing out "indirectly." An Aura, Equipment, or Fortification that phased out indirectly won't phase in by itself, but instead phases in along with the permanent it's attached to.