Sundial of the Infinite and end of turn effects

Question

If I use Sarkhan, the Dragonspeaker first ability, and before the end of my turn use Sundial of the Infinite. Does he stay a 4/4 indestructible dragon until my next turn? And if yes does that mean he cannot lose loyalty as he is a creature and is indestructible?

Answer 1

No. Sarkhan stops being a dragon when your turn ends. It doesn't matter that you have ended your turn "early" using the Sundial - the turn still ends.

The reminder text on Sundial of the Infinite makes this clear:

{1}, {T}: End the turn. Activate this ability only during your turn. (Exile all spells and abilities on the stack. Discard down to your maximum hand size. Damage wears off, and "this turn" and "until end of turn" effects end.)

Answer 2

Sarkhan would stop being a dragon

Sundial of the Infinite reads:

1, T: End the turn. Activate this ability only during your turn. (Exile all spells and abilities on the stack. Discard down to your maximum hand size. Damage wears off, and "this turn" and "until end of turn" effects end.)

Italicized text on cards is reminder text. It is redundant to the actual rules text, but is designed to clarify exactly what a card is intended to do, or introduce the meaning of a keyword or rules term that a player might not recognize.

Sarkhan's first ability reads:

+1: Until end of turn, Sarkhan, the Dragonspeaker becomes a legendary 4/4 red Dragon creature with flying, indestructible, and haste. (He doesn't lose loyalty while he's not a planeswalker.)

So when Sundial of the Infinite's ability resolves, Sarkhan stops being a dragon, and goes back to being a planewalker.

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In more detail

Ending the turn with a spell or ability is covered by rule 716

716. Ending the Turn

716.1. Some cards end the turn. When an effect ends the turn, follow these steps in order, as they differ from the normal process for resolving spells and abilities (see rule 608, “Resolving Spells and Abilities”).

716.1a If there are any triggered abilities that triggered before this process began but haven’t been put onto the stack yet, those abilities cease to exist. They won’t be put onto the stack. This rule does not apply to abilities that trigger during this process (see rule 716.2).

716.1b Exile every object on the stack, including the object that’s resolving. Remove all creatures and planeswalkers from combat. All objects not on the battlefield or in the command zone that aren’t represented by cards will cease to exist the next time state-based actions are checked (see rule 704, “State-Based Actions”).

716.1c Check state-based actions. No player gets priority, and no triggered abilities are put onto the stack.

716.1d The current phase and/or step ends. The game skips straight to the cleanup step; skip any phases or steps between this phase or step and the cleanup step. If an effect ends the turn during the cleanup step, a new cleanup step begins.

716.2. No player gets priority during this process, so triggered abilities are not put onto the stack. If any triggered abilities have triggered since this process began, those abilities are put onto the stack during the cleanup step, then the active player gets priority and players can cast spells and activate abilities. Then there will be another cleanup step before the turn finally ends. If no triggered abilities have triggered during this process, no player gets priority during the cleanup step. See rule 514, “Cleanup Step.”

716.3. Even though the turn ends, “at the beginning of the end step” triggered abilities don’t trigger because the end step is skipped.

This is a lot of text, but the main gist of it is that anything that was waiting to happen goes away, and the game skips straight to the 'cleanup step'.

What is the cleanup step? I'm glad you asked!
A turn has 5 phases:
Beginning Phase (Untap, Upkeep, and Draw)
First Main Phase
Combat Phase
Second Main Phase
Ending Phase

The Ending Phase has two parts: The End Step and the Cleanup Step.

The End Step (not the End Phase) exists so that delayed triggers that happen "At the beginning of the next end step" have a clear time to happen. Like the Upkeep Step, it only matters if a card is making it matter.

513. End Step

513.1. The end step has no turn-based actions. Once it begins, the active player gets priority. (See rule 116, “Timing and Priority.”)

513.1a Previously, abilities that triggered at the beginning of the end step were printed with the trigger condition “at end of turn.” Cards that were printed with that text have received errata in the Oracle card reference to say “at the beginning of the end step” or “at the beginning of the next end step.”

513.2. If a permanent with an ability that triggers “at the beginning of the end step” enters the battlefield during this step, that ability won’t trigger until the next turn’s end step. Likewise, if a delayed triggered ability that triggers “at the beginning of the next end step” is created during this step, that ability won’t trigger until the next turn’s end step. In other words, the step doesn’t “back up” so those abilities can go on the stack. This rule applies only to triggered abilities; it doesn’t apply to continuous effects whose durations say “until end of turn” or “this turn.” (See rule 514, “Cleanup Step.”)

The Cleanup Step is where everything that happened "Until end of turn" wears off. While the End Step only happens once each turn, and any "at the beginning of the end step" triggers that appear after it passes by will wait until the end step of the next turn, the Cleanup Step has to happen, and it continues to happen until there's nothing left to clean up.

514. Cleanup Step

514.1. First, if the active player’s hand contains more cards than their maximum hand size (normally seven), they discard enough cards to reduce their hand size to that number. This turn-based action doesn’t use the stack.

514.2. Second, the following actions happen simultaneously: all damage marked on permanents (including phased-out permanents) is removed and all “until end of turn” and “this turn” effects end. This turn-based action doesn’t use the stack.

514.3. Normally, no player receives priority during the cleanup step, so no spells can be cast and no abilities can be activated. However, this rule is subject to the following exception:

514.3a At this point, the game checks to see if any state-based actions would be performed and/or any triggered abilities are waiting to be put onto the stack (including those that trigger “at the beginning of the next cleanup step”). If so, those state-based actions are performed, then those triggered abilities are put on the stack, then the active player gets priority. Players may cast spells and activate abilities. Once the stack is empty and all players pass in succession, another cleanup step begins.

Ending the turn skips the end step, but does not skip the cleanup step.