Short answer: Use the former-latter when talking about two things. And use the first, second, third when referring to an item in a list of three.
Traditionally, the former and the latter are used only when referring to two items.
This is upheld by multiple definitions in thefreedictionary. See its entries for former amd for latter. Notice the usage notes, especially the ones given in the definitions by Collins.
The Oxford Dictionary online (ODO) vigorously supports this usage. I quote in full. Notice the last sentence.
Traditionally, former and latter are used in relation to pairs of items: either the first of two items (former) or the second of two items (latter). The reason for this is that former and latter were formed as comparatives, and comparatives are correctly used with reference to just two things, while a superlative is used where there are more than two things. So, for example, strictly speaking one should say the longest of the three books but the longer of the two books. In practice, former and latter are now sometimes used just as synonyms for first and last and are routinely used to refer to a contrast involving more than two items. Such uses, however, are not acceptable in good English style.
The Oxford Learners Dictionary defines the former as
used to refer to the first of two things or people mentioned
and latter as
being the second of two things, people or groups that have just been mentioned, or the last in a list
Note that Oxford here does not have a usage note. So I think it is a disservice to learners to omit a usage note, or to provide a definition that contradicts the one given in its own ODO.
Given the strong note in the ODO, the strong usage note by Collins, and the definitions given by the other dictionaries, I would go with using the former-latter only when talking about two things. And use ordinal numbers, first, second, third when referring to an item in list of three.