I have some doubts about the end step.
For example, if at the beginning of the end step of my opponent's turn I cast Yeva, Nature's Herald, can I cast another creature after it resolves?
And in Meren of Clan Nel Toth's case, after a creature returns to my opponent's field with her trigger, can I still at the end of the turn destroy this creature with an instant?
After a spell or ability resolves (except for mana abilities) the active player receives priority. The End step continues. No step or phase, in which a player receives priority, ends, until all players pass priority in succession. This means any step or phase except the untap and cleanup steps.
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In both cases, players will still get priority to cast instant spells and activate abilities after Yeva or Meren's last ability resolves; the end step ends only after all players pass while the stack in a row, not when a spell or ability resolves (C.R. 116.3b, 116.4, 500.2, 116.1a-b).
Yeva's second ability starts to apply as soon as it enters the battlefield (C.R. 611.3b, 112.6). Once it starts, you can cast green creature spells (in addition to instant spells) during the same end step in this scenario (C.R. 116.1a, 601.3b, 702.8a, 116.3b). And after Meren's last ability resolves, you will still have priority to cast instant spells (such as Murder) before the end step ends (C.R. 116.3b, 116.1a).
For example, if at the beginning of the end step of my opponent's turn I cast Yeva, Nature's Herald, can I cast another creature after it resolves?
And in Meren of Clan Nel Toth's case, after a creature returns to my opponent's field with her trigger, can I still at the end of the turn destroy this creature with an instant?
Awesome avatar provided by Krashbot @ [Epic Graphics].
Yeva's second ability starts to apply as soon as it enters the battlefield (C.R. 611.3b, 112.6). Once it starts, you can cast green creature spells (in addition to instant spells) during the same end step in this scenario (C.R. 116.1a, 601.3b, 702.8a, 116.3b). And after Meren's last ability resolves, you will still have priority to cast instant spells (such as Murder) before the end step ends (C.R. 116.3b, 116.1a).
EDIT (Jan. 8, 2019): Correctness edit.