An adjective clause tells something about the noun or pronoun in the sentence. It provides some of the required information which is essential for the sentence. An adjective clause begins with relative pronouns or relative adverbs. They provide additional information. A subject and a verb is a part of an adjective clause. In the above sentence, 'that is mailed today' is the adjective clause.
For "He lived a year in a minute" I think it means that all of a sudden he looks very old, is tired, or maybe time went by really fast? Like I said I am not 100% sure so don't take my word for it. Heck I am not 10% sure, more like I am 5% sure, 20% at the most. Sorry if I am wrong.