You switch between [title] and [task] in your naming scheme (example: 'Jeweller'/'Blacksmith' vs 'Smelting'/'Milling'). Also, you have some less-common names ("Apiarist") and some more-common names ("Blacksmith") - I'd focus on one or the other. And I'd lean to the less-common (which makes it sound archaic), but make sure you have plain-english descriptions very visible on your interface.

Here's some ideas:

[Edit:] Bah, formatting issues. Made the chart an image instead.

Another thing to note is the difference between specialized roles and generic roles. For example, you have "Blacksmith" and "Weapon crafting" and "Armor crafting". Are they subclass specializations or entirely separate skills? For example, I'd think Saddlemaking would be a subset of Leatherworking (tanning). Likewise, Tailor and Weaver, while not identical, seems like one would be a superset of the other. I'm not positive about that, though.

When towns get bigger, more skilled individuals can go into specialization. If a town is smaller, you'd need people to be jack-of-all-trades - in a small town, the blacksmith better know how to make a sword, sharpen a plow, and forge horseshoes. In a huge city, he can specialize not just in one type of product, but even one type of material - goldsmiths and silversmiths can co-exist in specialization if they live in an area large enough to still get plenty of work each.

In the modern day, I know a contractor who decided to stop doing general contracting as he got older, and now only does garage doors. He can go in, knock the job out, and charge $5000 for it. On the other hand, in the old days, even farmers needed to know the basics of iron working to make their own basic tools. I know a farmer, in his 90s now, who still has some of his old iron-working tools in his workshop from way back when.

This is a quite big list of skills, and on many I don't really see how one could conceptually "level" or how once could conceptually produce better output since it depends on the inputs.

Can't you batch together a few of these (without losing "game value")? Maybe with specilalisations or "craft plans", so you can for example buy leatherworking if you have tailoring, so you can tailor cloth and leather?

Dyeing - Amount depends on the amount of ingredients, how do you produce more dye? Need to gather more flowers or acorns, or ... stuff.

Apiarist - Does not tend bees (you explicitly said so) but just collects honey combs in forest. Which is basically "gathering". You can't make more honey out of the same amount of honey combs.

Milling - Same. Amount depends on the amount of wheat (or some other cereal), which is generated by farming, or well... some form of gathering. Also a level 50 miller can't make more flour than a level 1 miller, obviously.

Tannery - Depends on the amount of hides (... animal tending) and involves the actual tanning, but otherwise pretty much identical to tailoring.

Saddle making - Subclass of tannery.

Cheese making - Depends on the amount of milk. So... animal tending, or gathering. Or, like brewing beer and baking bread, cooking or foraging in a wider sense.

'Law' - do you mean the giving and executing of laws (i.e. governments creating laws), or the study and debating of of law (i.e. lawyers)?

'Theology' is distinct from 'Religion'. Theology being specifically the study of scripture and the study of the nature of God. For example, a pastor might not be a theologian, but a teacher usually would be. (Theologian = biblical scholar, not necessarily a priest). It's the christian version of a philosopher.

Specific questions:
- Tannery - shouldn't it be Tanning? (I'm not a native English speaker)

Yes, sorry. [Tannery] is the location, [Tanning] the task, [Tanner] the occupation.

I made a few other mistakes. For example, Wikipedia seems intent on arguing that 'Cobblers' only repair shoes, they don't make them (a Cordwainer makes shoes, apparently). 'Cordwainer' as a term isn't at all common in the United States, but 'Cobbler', while no longer used in practice, is more well-known from fairy tales and history. However, Cordwainer fits very well into the archaic-sounding titles and might be a better fit for your game.

Blacksmith - is it really a name of a task? Not just a profession? Isn't it "blacksmithing" or something?

Another mistake. Yes, 'smithing', 'forging', 'crafting', 'smelting' would be more likely the task name. 'blacksmithing' wouldn't sound correct.

- Milling (flour making) - should I use just "Milling" maybe? Is it sufficiently clear that it is to produce flour?

Yes you can - but bear in mind that there are more kinds of mills than just wheat-mills.

- Apiarist/Beekeeping - I have a problem here, you actually go to a forest and gather honey combs, then you extract the honey combs and make honey (both these actions use "Apiarist" skill). The thing is, you techically do not keep any bees, so "Beekeeping" is not correct/is misleading.

'Honey forager', maybe? I'm not aware of a specific English title for that. If someone finds a honey-bee hive in the woods, they (in real life) used to just relocate it to a more convenient spot on their own property.

I'd use 'Apiarist' anyway, just because it sounds cool.

Should I use more "___ making" or "___ crafting"?

It's a matter of aesthetics - both are acceptable.

Personally, I dislike seeing a long list of "______ [word]" regardless of what [word] is. I, as a non-professional hobbyist game designer, would prefer single-words to double-word tasks, unless the single-words aren't descriptive enough. Tossing in a few "______ [word]" into the list is fine to me, but then I'd vary up what the [word] is, depending on context.

Instead of:
Bread making
Sword making
Armor making
Beer making

While those are acceptable, for artistic reasons I'd replace it with:
Baker
Sword-crafter
Armor-forger
Brewer

...avoiding using the same word more than once if I can help it.

Smelting, Jewelry, Blacksmith - These are special case, generally you use blacksmith skill to do everything related to iron, EXCEPT smelting iron ore into iron ingots shoich use smelting. Similarly the same smelting skill is used to smelt precous ores by the jeweller to make jewelry. I found out it's quite confusing to players... I wonder, should I remove smelting and just use blacksmith/jewelry for ingots as well?

There are game design reasons why you might want multiple different players to have to participate together to produce a final product. You'd have to figure out why it's confusing. Is it actually "confusing", or do they just not like it? What don't they like about it - is it too time-consuming, do they feel the 'smelting' skill is too limited in use that they are wasting skill points on it?

A general rule of thumb in game-design is that if a player tells you something is wrong, consider it carefully and think through it. But if a player tells you how to fix it, cover your ears and don't listen. Players make bad designers, but they do know when they aren't enjoying something.

You have to consider as a designer what purpose the skill has, and whether you should expand its purpose (i.e. add more features and abilities to the 'smelting' skill), eliminate its purpose (e.g. remove iron ore and smelting entirely), or consolidate its purpose (i.e. merge it into blacksmithing).
What you do would be dependent on how your game works, and what you think as a designer would be 'best' for the game and the players as a whole. 'Best' doesn't always mean most enjoyable immediately - sometimes undesirable (from a player-perspective) design decisions make the game overall more enjoyable.

Anyway, here is an improved list of skills (switched to "task"):
Digging
Mining
Wood cutting
Hunting
Fishing
Baking bread
Cheese making
! Apiarist !!! 'Honey gathering' might be a clearer.
Oil making
Milling
Carpentry
Smelting
Forging
Jewelry Jewelry making ("Jewelry" is the product, not the task)
Tanning
Weaving
Dyeing
! Tailor !!!
Shoe making
Bricks making Brick making (no 's' after 'brick')
Pottery making
Paper making
Brewing beer
Brewing wine
Candle making
Saddle making
Weapon crafting
Armour crafting

That list looks good and makes sense in English.

It's confusing because all other crafdting skills cower the whole workshop, while Jeweller/Balcksmith have a subskill of sort that affects only smelting. Plus, when I'm using "Blacksmith" the natural expectation is it to contain *all* the skills a blacksmith needs... Above I changed Blacksmith to Forging so Forging+Smelting would sound better I suppose (but what about Jewelly, it still needs a Smelting skill.
Of course I could just discard Smelting and include it into Forging/Jewelry.

In that case, it probably would be better to just give Blacksmithing the ability to smelt iron ores, and to give Jewelry Making the ability to smelt gold ores. Or, to just remove iron ingots and gold ingots and have Blacksmiths forge equipment directly from the ores to remove an unnecessary step.

'Honey forager' is one option. 'forager' implies gathering, but can include processing.

'Honey harvesting' or 'Honey extraction' also would work.

'Beehive processing' or similar variations would de-emphasize honey specifically.