Genie,

surely Adeste fideles was not composed in old Roman times, but the times from Caesar an Cicero to Tacitus are quoted as the Golden ones, and language use of the Golden Aera is accepted as the Standard. Middle Latin as spoken in Medieval times has deteriorated, and better authors tried to write in the classical usage.
Here the adjective laeti must be used, because the fideles are full of joy and are triumphant. The conjunction et is, especially in poetry, often omitted.
In English you must insert "and" because of the metre. In German it is no problem, because we have 1 syllable more: "fröhlich triumphierend", so we dont need an "und".

Jim,

It is one of the mysteries of German usage. "Ich bin Berliner" = I'm living in Berlin, I'm born in Berlin" etc. But JFK's quote "Ich bin ein Berliner" has a slightly different meaning, considering the words spoken before: I'm one of all you freedom loving people of Berlin. With this German sentence he ended his speech using a climax, and the word "ein" gives it more stress. So his language use was considered appropriate by all German listeners. You could see tears flowing at some places.

Wilfried