1. I have a faerie miscreant in play. Cast another faerie miscreant.. can the opponent fatal push the miscreant in play to prevent me from drawing a card?
2. End of opponent's turn. I cast a quickling to return a faerie miscreant to hand. Can the opponent respond by fatal push the miscreant, so I cannot return it to hand?
1. Faerie Miscreant's enters-the battlefield-ability checks whether "you control" a creature other than Faerie Miscreant that is "named Faerie Miscreant"—
when Faerie Miscreant enters the battlefield (if "you don't", the ability won't trigger) (C.R. 603.4), and
when that ability would resolve (if "you don't", the ability won't resolve and you won't draw a card) (C.R. 608.2a).
2. You don't choose which creature you control other than Quickling, if any, to return to its owner's hand with Quickling's last ability until that ability resolves (C.R. 603.5, 118.12a). In general, however, if you choose such a creature in advance, you will be bound to that choice unless another player intervenes (C.R. 722.2a-c; for sanctioned tournaments, see M.T.R. 4.2). See also this thread and this thread.
EDIT (Jan. 24, 2020): Some rules were renumbered with Core Set 2020.
EDIT (Jun. 4, 2020): Edited, including because one rule was renumbered with Ikoria: Lair of Behemoths.
1. I have a faerie miscreant in play. Cast another faerie miscreant.. can the opponent fatal push the miscreant in play to prevent me from drawing a card?
2. End of opponent's turn. I cast a quickling to return a faerie miscreant to hand. Can the opponent respond by fatal push the miscreant, so I cannot return it to hand?
Nexus MTG News // Nexus - Magic Art Gallery // MTG Dual Land Color Ratios Analyzer // MTG Card Drawing Odds Calculator
Want to play a UW control deck in modern, but don't have jace or snaps?
Please come visit us at the Emeria Titan control thread
2. You don't choose which creature you control other than Quickling, if any, to return to its owner's hand with Quickling's last ability until that ability resolves (C.R. 603.5, 118.12a). In general, however, if you choose such a creature in advance, you will be bound to that choice unless another player intervenes (C.R. 722.2a-c; for sanctioned tournaments, see M.T.R. 4.2). See also this thread and this thread.
EDIT (Jan. 24, 2020): Some rules were renumbered with Core Set 2020.
EDIT (Jun. 4, 2020): Edited, including because one rule was renumbered with Ikoria: Lair of Behemoths.
Nexus MTG News // Nexus - Magic Art Gallery // MTG Dual Land Color Ratios Analyzer // MTG Card Drawing Odds Calculator
Want to play a UW control deck in modern, but don't have jace or snaps?
Please come visit us at the Emeria Titan control thread