Learn Finnish: Seremonian loppuessa presidentti antoi minulle kunniamerkin. - When the ceremony ended, the president gave me a decoration of honour.

You would add the uninflected pronoun itse immediately before the noun, making it ...itse presidentti antoi.... When used as an intensifying appositive to mean 'the person himself', itse does not take any endings, even if the noun it emphasizes happens to be inflected.

Why is seremonia in the genitive form (seremonian) here?

It acts as the subject of the temporal construction loppuessa (which translates to 'when ending' or 'upon the ending of'). In this structure, known as the second infinitive, the noun performing the action must be placed in the genitive case.

Could I say Kun seremonia loppui instead of Seremonian loppuessa?

Yes, kun seremonia loppui is the exact equivalent using a standard subordinate clause. The -essa structure used here is simply a more compact, slightly more formal way to express that two events happen simultaneously or consecutively.

What parts make up the word kunniamerkin and why does it end in -n?

It is a compound of kunnia (honour) and merkki (mark, sign, or badge). It takes the -n ending here because it is a singular total object; the president gave a single, complete decoration to you, so the object takes the genitive-accusative form.