As others have mentioned, this depends a lot on what the rules behind turning into a zombie are. Meaning, this could change from world to world.
If becoming a zombie it is the result of a pathogen, then the nature of the infection will dictate the feasibility of zombies becoming a source of food.
Consider the core options in a world infested with zombies:
- Contaminated food: Food that had been tainted by zombified remains or insects spreading the infection.
- Direct source of food: Zombie meat from a zombified animal or human.
- Indirect source of food: Animals or plants consume zombies as direct sources of food or contaminated sources of food (Water contaminated by zombified remains also counts).
Depending on how the agent of infection is spread and its fortitude, it might be possible that certain animals, plants and insects could be able to withstand the contamination and detoxicate the food or water. Conversely, some animals, plants and insects could increase the potency of the agent potentially mutating it into something worse. This, again, depending on how that particular world works.
If becoming a zombie is the result of a curse or magic like in the film The Serpent and the Rainbow, the rules of what is needed, how it affects the body and how it is transmitted will determine the edibility of any zombified beings.
In the particular case of the film mentioned, it appears that a drug is used to produce the desired effect. Some drugs must be injected directly to the blood stream for them to work, while others have to be ingested, this will also become a factor on edibility. Some components can be eaten without producing the effect, so in that case it could be safe.
More magical realms would require additional analysis on what happens to cursed or enchanted beings that get eaten. Interestingly enough, despite all the fairy tales there is little exploration on this aspect of magic.
However, worlds with magical-based zombies might have an edge if there are spells or potions which revert them back to their former selves. Notice that this might differ a little from an uncontrolled outbreak scenario, since magical zombies tend to be more controlled and those who tame them have developed means to keep themselves from becoming zombies. Even the film mentioned shows that zombies are easily manipulated by those who turn them.
If becoming a zombie is the result of a parasite (like real life ant-zombies infected by a fungus) then it will depend on the characteristics of the parasite itself. In the particular case of the fungus that infects the ants, the parasite only attacks a particular species, which might make it relatively safer to consume (if the zombified animal was not a human, of course).
Like other parasites, it is possible to use methods to cook such meat by ensuring the death of the parasite before consuming the food; however, how safe it really is can only be determined by how the parasite reproduces and propagates.
An example of a work of fiction where zombification has been treated as a parasite with very specific rules on its propagation would be "Higurashi Outbreak". Animals are not covered in that particular scenario, so it would be safe to consume any meat produced by an animal, given other qualities of the parasite explained in that film.
With that in mind, everything really comes down to the rules of the particular world which is under a zombie siege. A work of fiction that does address food and resources in a zombie post-apocalyptic world is the web comic Zombie Ranch. In this particular instance, animals and humans can become zombies and eating zombies is safe, despite the taste. In this world, humans are forced to become vegetarians. Additionally, zombie blood is not contagious and they can be used to produce medicines that extend the life of the living and other products.
Having said that, zombies could be used for labor depending on how sturdy they are in the world in question. They could also be used for theoretical perpetual motion machines, these two under the provisions of the rules of the world, since zombies that might not consume flesh (or brains) might eventually lose energy, become inactive and break-down.
Despite the kind of zombie, they could be leveraged for hunting (like how hunt dogs are used) but this would require to have a certain degree of control over the zombies, which would vary from reality to reality. Additionally, depending on how the zombification process happens, it might not be a good idea to risk to infect your food by performing said actions.
Back to the issue of having a safe way to eat zombies. If we were to assume all the worlds to which this question would apply are similar to ours, then there is one simple answer: Pasteurization.
Pasteurization would address zombies that have been turned due to a pathogen and parasites, since it is a process which kills microbes (bacteria) in foods and drinks. If you were also to assume that eating beings that have been exposed to magic as a non-issue (meaning that magic would not cause any damage to those consuming magically treated food) then, that addresses the main issue.
Pasteurization is easy enough to perform without a lot of technology, since it was discovered in 1864 by Pasteur who noticed that heating beer and wine would kill most of the bacteria in it, leading to a process that achieves eliminating pathogenic microbes. Since this process is used widely in food processing industries and the dairy industry, it is not a stretch that ranchers might be able to survive a zombie apocalypse by applying knowledge of food preservation that they already possess, making a "zombie ranch" more plausible.
Now, on to the other aspect of the question: resources. Being able to use the zombies as other resources would depend on several factors such as the infrastructure that is left in the world after an outbreak and the properties of the "undead" creatures, as previously discussed; however, there are similarities in all worlds where there is a concept of a zombie which is the usage of these undead fiends against other humans (It comes down to weaponizing them).
Louis Pasteur, saving the multiverse from zombie apocalypses since 1864.