The two recipes that do NOT require an Alchemist Table, require you to hold the Mortar and Pestle in your hand slots, similar to Frying Pan or a Glass-Blowing Rod. Lets call this the first tier of alchemy.
Second tier is more or less building an Alchemist Table, then crafting the following and placing them on the table:
https://ringofbrodgar.com/wiki/Retorthttps://ringofbrodgar.com/wiki/Tripod_Burnerhttps://ringofbrodgar.com/wiki/Testtube_RackThis will unlock "Mineral Calcination" and "Measured Distillate" -processes, alongside "Mushroom Decoction" -elixir.
Third tier will start requiring expensive materials - one-time cost for two advanced tools requires "precious metal" (ie. gold or silver) and utilizing them consumes high amounts of Mercury and/or Lye.