Coagulants for Tofu or else I'm new when it comes to vegan cooking and until recently began experimenting and researching with regards to the commonly used or appropiate coagulants whether acid or salt based to best make my own crafted tofu.

So I've got the following questions:

Is calcium sulfate dihydrate the same as the regular calcium sulfate, also known as Gypsum used for food processing?

On the other hand, are all of the following coagulants safe to be used for culinary purposes per se, meaning as simply getting the chemical with the stablished name from a supplier without it having any additional variations such as the "dihydrate" form explained above, or do they require to have a "Food grade" stamp or "for culinary use" tag necessarily?

-Calcium Sulfate.

-Magnesium Sulfate "Epsom Salt".

-Magnesium Chloride (In this case if it also needs to be branded as "Nigari/Bittern").

-Calcium Chloride.

And finally if you could please please clear out which are animal sourced and which are plant derived or if they are all synthetic. That would be really helpfull.

Thankyou deeply.
To add to @moscafj's answer:

There is a saying "There's no such thing as poison, there's only dose". If you take too much of anything, it can be hazardous to your health or wellbeing. Your body needs both calcium and magnesium to function properly, but taking too much can cause you issues as well. 

Calcium chloride and magnesium chloride can cause burns if ingested as a solid,or if touched with wet hands while in the powder form, as well as "gastric distress, and vomiting". These mostly taste like ordinary table salt (sodium chloride), and calcium chloride is often used to replace the sodium in "low sodium" foods. These salts are hygroscopic and will absorb water from the air rapidly unless kept tightly sealed.

Magnesium sulfate is used to treat a range of health problems, including constipation, but too much can also result in hypocalcaemia (low blood calcium) and resulting depression of heart function. MgSO4 is also bitter and unpalatable, but that doesn't stop people drinking it.

The chemical forms of these various compounds don't matter at all unless you happen to be into chemistry and are working out something quantitative in terms of molecular amounts or Moles as they are known. If you see a term containing the word hydrate, this means water of crystallization, which is a chemistry term for the naturally occurring amount of water that is found in the crystalline form. The exact number of water molecules associated with each molecule of the chemical is indicated by the prefix, which might be mono (1), di (2), or a number of other prefixes and varies according to the chemical and which forms it can take. For cooking purposes the hydrate form is the same as anhydrous (without water), though the anhydrous is often more expensive and will usually absorb water from the air rapidly to form the hydrate.