Well in English, when you want to pluralize something it depends on the type of word and its roots. But for acronyms and abbreviations you just slap an S on the end. Unless the word ends in an s in which case you slap es on the end. So presumably it would just be TARDISes.

Consequently, that explanation also answers the second point.

The jokester in me wants to say TARDIS → TARDES by analogy of penis → penes but the fact of the matter is that Time and Relative Dimensions in Space doesn’t really pluralize even when it isn’t abbreviated