Last time I checked, they are considered "not alive" when outside of a host, and "alive" when inside a host.
About size: "Genome size varies greatly between species. The smallest—the ssDNA circoviruses, family Circoviridae—code for only two proteins and have a genome size of only two kilobases;[61] the largest—the pandoraviruses—have genome sizes of around two megabases which code for about 2500 proteins"