Hello, MAESTRO31, and welcome to the Grammar Exchange.
Judging by your user name, I'm inclined to believe that Spanish is your native language, and this accounts for your confusion. In Spanish, "equipo" (equivalent to the English equipment) can be used to refer to a single piece of equipment, and we use the plural "equipos" or the singular "equipamiento" to refer to a whole set formed by different pieces of equipment. Well, that is not the case with English.
In English, equipment is an uncountable, and therefore singular, noun. Being non-count, it does not refer to a single piece but to a whole set of equipment, or at least to a certain number of devices, appliances or mechanisms.
Therefore, the sentences below are INCORRECT (next time, please number them for ease of reference):
-These 3 equipment are always maintained.
-Each equipment is checked before using it.
-We have a set of 5 equipment which we don't have their specific spare parts.
-We have 5 equipment which we don't have their specific spare parts.
In line with my explanation above about uncountable nouns being always singular, in the sentence below the term "equipment" is grammatically singular though it may refer to more than one component.
-The equipment is maintained according to its fault rates.
I have to say that there are other mistakes in your sentences above (as well as in the others), with some of them having nothing to do with the number of "equipment," for example:
- be always maintained does not sound like the best collocation. I'd say something like be maintained on a regular basis.
- I'd change before using it to before being used.
- the structure which we don't have their specific spare parts is ungrammatical: you should eliminate "we" or change to "for which we don't have the specific spare parts."
- There are other mistakes of number agreement which are based on your misconception about the word "equipment": if "equipment" is singular, then the auxiliary "don't" and the possessive "their" are wrong and should be changed to "doesn't" and "its."
The sentence "All of the equipment must be maintained according to their fault rates" is only wrong because of the use of "their" instead of "its." All is fine to refer to a noncount noun.