1a) No. Muldrotha only gives you permission to cast spells from your graveyard on your turn and Vedalken Orrery does not make your opponent's turn your turn.
1b) Unless of course it is your turn. Then yes, you can do this.
(you didn't say whose turn it was so I answered both possibilities)
2) Yes. Since you are casting it (if it is not a land) you can pay alternate costs, such as Morph, when casting it.
Can I counter their spell by casting Glen Elendra Archmage from my graveyard and activating her ability?
No, beause Muldrotha's effect only works during your turn. Flash does not change that. Though you can flash out cards from your graveyard during your turn with those cards.
Can I cast a card with morph from my graveyard as a facedown morph creature if I have Muldrotha in play?
Yes. There is no alternative cost imposed by Muldrotha, and you are casting the spells, so you can still apply an alternative cost, like morph, if one is available.
I have Vedalken Orrery in play.
Opponent casts a noncreature spell.
Can I counter their spell by casting Glen Elendra Archmage from my graveyard and activating her ability?
Can I cast a card with morph from my graveyard as a facedown morph creature if I have Muldrotha in play?
thanks
1b) Unless of course it is your turn. Then yes, you can do this.
(you didn't say whose turn it was so I answered both possibilities)
2) Yes. Since you are casting it (if it is not a land) you can pay alternate costs, such as Morph, when casting it.
No, beause Muldrotha's effect only works during your turn. Flash does not change that. Though you can flash out cards from your graveyard during your turn with those cards.
Yes. There is no alternative cost imposed by Muldrotha, and you are casting the spells, so you can still apply an alternative cost, like morph, if one is available.
Former Rules Advisor
"Everything's better with pirates." - Lodge
(The Gamers: Dorkness Rising)
"Any sufficiently analyzed magic is indistinguishable from science."
(Girl Genius - Fairy Tale Theater Break - Cinderella, end of volume 8)