The other player does not have the authority to determine that
The DM does, though. The player is offering you a decent suggestion, in terms of being careful not to offend your deity.
I wonder if there is a game mechanic of possibility for cleric to lose
powers due to inappropriate behaviour.
No, there isn't a mechanic like that in D&D 5e.
- Note: there is a tradition from previous editions that clerics and
paladins, any divine caster, can lose access to spells and class features after violating some code of conduct, which might influence the DM at this table. You need to ask the DM: is this convention active at this table with this DM? If so, that's a house rule that you need to be aware of since it is the reality of your situation with this DM's world. (Credit to @Revolver_Ocelot for raising that point)
Your DM may use this episode to have your deity communicate with you
How your deity responds to your various actions as a cleric is completely in the hands of the DM, who plays all of the other beings in the game - mortal and immortal, good and bad, deity and dog. Anyone who is not one of the PCs, the DM plays the role of.
You have a fine opportunity to role play that interaction with your DM (who can act as the deity, Sune) if the DM decides to have Sune send you a message of approval or disapproval. Removing access to a spell is one way (of many) that a deity may communicate with you. It's up to the DM.
Role playing suggestion
Mention to the DM that when your cleric prays to prepare spells during the next long rest, your cleric is open to and listening for any indication from Sune that your actions were OK, or were not OK. It never hurts to ask.
The DM will or won't go along with that. I have used this as a DM with some frequency in this edition, and in previous editions. I have also asked for stuff like this, as a player, during spell preparation time. Some DM's like this idea better than others and will drop hints as a response.
Interrogations as a cleric PC: Zone of Truth
The second level spell called "Zone of Truth" can be helpful to you in asking and getting answers to questions without beating on the NPCs. I've played a variety of clerics, and find that this spell is a way to run a question and answer session with no need for violence. There is risk:
- It offers a saving throw.
- If the target is intelligent enough and there is hostility to the
point where violence is an option that makes some narrative sense,
the spell may not help. They can refuse to provide an answer.
(Pleading the fifth) (@fabian, credit for sharing that point)
It is a second level spell; it needs at least a third level cleric to prepare and cast it. The points above illustrate the requirement for the cleric to be somewhat clever in how they ask questions while using this spell. It may be beneficial to use a persuasion attempt to encourage them to be more cooperative. That will be very situation dependent.
Zone of Truth
You create a magical zone that guards against deception in a 15-foot-radius sphere centered on a point of your choice within range. Until the spell ends, a creature that enters the spell’s area for the first time on a turn or starts its turn there must make a Charisma saving throw. On a failed save, a creature can’t speak a deliberate lie while in the radius. You know whether each creature succeeds or fails on its saving throw.
An affected creature is aware of the spell and can thus avoid answering questions to which it would normally respond with a lie. Such a creature can be evasive in its answers as long as it remains within the boundaries of the truth. (PHB, p. 289)