uneventfully; without incident; peacefully
Describes a situation or event that passes without any trouble, accident, or notable occurrence. Often used when something was expected to be problematic but ended smoothly.
The ceremony ended without incident.
The day passed uneventfully.
平穏に means 'peacefully' or 'tranquilly', focusing on a calm state. 何事もなく is more about the lack of incidents or problems.
Standard kanji spelling.
Variant using the kanji 無 for な.
From 何事 (なにごと, 'anything; something') + も (inclusive particle) + なく (adverbial form of ない, 'not'). Literally 'without anything happening'.