Yhyjyk

I recently bought a product, let's say a car, with limitations intentionally introduced to the design, for example an electronic speed limiter. Being a bit of a tinkerer, I messed with my model until I figured out how to remove this limitation (i.e. remove the electronic speed limiter). If I were to publish this information online, telling other people how to modify their models, would it be legal?

As another example, let's say I figured out how to raise the power on a brand-name microwave, or increase the cooking speed of a rice cooker. Provided the end result isn't in violation of any particular safety laws (and assume for the purpose that they do not), can I legally publish the information of how to do so?

In my opinion, you are totally free to publish the information.

There are two areas of law that can be cosidered - private and public law.

In the private law area, you can be liable for revealing trade secrets, but only if you agreed to keep them by a contract. Trade secrets do not exist by themselves (there are minor exceptions, eg. in competition law, but those do not concern us), they must be protected by contracts. Another private limitations, like libel laws, won't apply here.
This is not uncommon, but not in cars - you can find clauses like these in software license agreements.

Then there is the public area. Is there any regulation, any policy of the state, that prevents you from publishing it? I am not aware you whole legal code of your state, but I doubt there is. It would be a harsh limitation of freedom of speech. Even if the modification could lead to illegal effect (like, modifying toy weapon to kill by rising its power...) it would be only illegal under very rare circumstances.

To conclude it - freedom of speech can be limited only if there is sufficient public interest to do so, and I don't see any.

I think it depends on whether you can be accused of revealing trade secrets or violating patents, as this kind of thing usually turns into an intellectual property battle.

Generally, you'd be protected from trade secret litigation if it can be shown that you discovered your secret modification on your own, and that you weren't granted access to any secret information by the owner of the product's intellectual property or any partners, employees, contractors, etc. of that owner. Patent infringement is mostly a problem if you're either making money off of the information, which you definitely don't want to do, or if it can be proven you're decreasing the value of their intellectual property.

In your car example, if the original company makes money by offering an option to remove that "electronic limiter" and you're showing people how to do it for free, you're in trouble. Otherwise, your obvious defense is that by offering people more options on what to do with their product, you may in fact be increasing the value of their intellectual property.

This isn't my branch of law, but if you're not making any money off of it, you're not getting too much visibility of your "published information" and you're not stopping people from paying the original company to get the same modification, you're probably safe. If in doubt, contact a lawyer.