Alberti bass is a kind of broken chord or arpeggiated accompaniment, where the notes of a chord are played in the order of lowest, highest, middle, highest. The C major chord (C E G) would be played (C G E G). The pattern is repeated.
Counterpoint means "point against point". It is combining more than one melodic lines that are very different from each other and move independent, but they still sound harmonious when played at the same time.