I see no problem with this kind of use for craft. Just make sure you dont let it go to becoming too generic of knowledge. - Gauss
These are reasonable examples of skill checks that make sense. I do this sort of thing all the time. If anything I might be a tad generous in this regard because I like to reward players for using skills in game.
Why wouldnt Alchemists be able to? They can learn any knowledge skill just like anyone can.
Well, of the examples you listed, using craft:alchemy to extract poison is the biggest stretch. I could argue that knowledge of chemicals and toxins does not require, nor even imply, that the alchemist knows how to handle dangerous animals.
In real life chemists who make anti-toxins don't tend to extract them from animals themselves. They actually have animal handling experts who do it for them. So on that call I can see the argument that it requires a nature and/or handle animal check.
Having another debate about rules. I say that craft checks, since they are int based, contain all related knowledge rolls about their craft. A carpenter could make a craft (Carpentry) roll instead of a knowledge (nature) roll to tell which trees make good, sturdy furniture or housing. An alchemist can make a Craft (Alchemy) roll to determine if they know how to extract poison or other alchemical ingredients from a creature without needing the creature's knowledge roll (Nature, Dungeoneering, Arcana, etc). Need a weigh in. Do Craft skills give you knoweldge in your field, or are you just a guy with tools who knows nothing of the actual practice?
The example I use is a Winemaker, (Craft Winemaking) would know how to grow the best grapes to make their wine. They don't need to have Knowledge Nature to identify the best types of grapes or the best fermentors, they would know as part of the craft.
In my opinion the solution should be somewhere in between. I think the craft skills should contain some knowledge of the matter at hand, however I would only allow it to a certain point. In most cases, I'd reasonably expect the PCs to have a few ranks in knowledges that are specifically used in their crafts (for more advanced uses anyway).
In your example, I don't think a knowledge(nature) check (by you or a party member) to actually know that the creature you are facing actually is the poisionous spider, whos extracts you've worked with on several occasion. Having worked with poisons, doesn't necessarily mean that you have been harvisting the poison glands yourself (and if you have, you should probably have a certain knowledge of those creatures).
Likewise, while I would expect a character with Craft(armor) to have some knowledge of different materials including special materials, I wouldn't extend that knowledge to knowing where and how to mine those materials unless he got the proper knowledge (such as dungeoneering).