Not at the moment, but in the future this will be possible.

Currently the effects you can brew come from a fixed list built into Alchemia, so effects added by other mods won't appear on the potion map.

Yes, with no code. Bases are defined in config/alchemia-brew-bases.json, which by default have a Water and Honey base.

To add an entry to the bases list, use the following template:

{
  "id": "milk",
  "fills": [
    { "item": "minecraft:milk_bucket", "levels": 4, "remainder": "minecraft:bucket" }
  ],
  "tint": "#F2F2F2",
  "texture": "minecraft:block/white_concrete",
  "instability_cap": 3,
  "effects": ["Regeneration", "Healing", "Saturation"],
  "dead_space": "field"
}

• fills: what item adds the base into the cauldron. Use either an item (with an optional remainder handed back) or a fluid (with an optional amount in millibuckets). levels is how much it fills by valid range is 1 to 4.
• effects: which effects can appear on this base's map. If blank it will attempt to add all effects (not recommended, but possible)
• dead_space: The type of noise that creates the "rings" (layered walls with gaps) or "field" (scattered patches).
• Other options are tint, biome tint, texture, instability cap and unbrewed result.
• Map layout: each base has its own potion map, so effects are in different places on each one.
• Display name: add a translation for alchemia.base.<id> (for example in a resource pack). Without one the name shows as the raw key.

Yes. Conditions are set via the server config alchemia-server.toml under [world_effects], in the conditions list. Each entry is set as Effect = condition, condition, ....

[world_effects]
conditions = [
  "Dolphins_Grace = rain",
  "Levitation@2 = above:90",
  "Levitation@3 = above:90, night",
  "Darkness = biome:minecraft:deep_dark",
  "Fire_Protection = biome:#minecraft:is_nether|minecraft:desert"
]

• Effect: an Alchemia effect name (Dolphins_Grace) or an effect id (minecraft:dolphins_grace).
• @level: with this suffix (Levitation@2), the effect can always be brewed, but that level and every level above it need the listed conditions.
• Conditions:
  • Weather and time: rain, thunder, clear, day, night.
  • Moon phase: full_moon, new_moon, moonlight:<0-1> (0.5 is a half moon). Moon conditions also need night.
  • Cauldron height: above:<y>, below:<y>.
  • Biome: biome:<id or #tag>|..., which allows the effect if the cauldron's biome matches any of the listed ids or tags.

To remove a condition, delete its line. To make every effect always brewable, empty the list (conditions = []).

Imbuements still apply. A brew imbued with bark or a biome item counts as being in that biome or at that altitude, so it can still activate biome- and height-locked effects. These items are configured separately in config/alchemia-imbuements.json.

Existing worlds have the condition list in the config file created with the world itself. You'll just need to edit the file in that world's serverconfig folder to change them.