You can store catsup, barbeque or chili sauce for 1 year unopened and 1 month after opening (stored in a cupboard). A store opened catsup in the refrigerator for up to 6 months as refrigerating would inhibit mold growth, but it seems to keep indefinitely in refrigerators. The vinegar in catsup (catsup) and sugar reduce mold growth. Even the most popular brands of catsup seem to separate a few drops of clear liquid during storage so I give the bottle a quick shake before using.
As to freezing, never tried that, but sounds reasonable as the ingredients in catsup are tomatoes, vinegar, sugar, salt and spices which should freeze well. If you freeze an unopened bottle, remember liquids expand when frozen and the bottle may break. Since catsup is a cooked product, I wouldn’t expect a lot of separation upon thawing as catsup doesn’t contain a lot of free water.