I have heard native English speakers using from time to time expressions like "I thought YOU WAS", or "I believed THEY WAS". I would like to know if this association is basically correct or just accepted due to the mass usage. If it is correct, is there a specific context when you can/should use this combination? Any formal rules?
The formal rule is: It is incorrect grammar. "was" is the third person singular form, and that's all there is to say about that.
However, "was" is used for other persons as well in several non-standard dialects of English, for example in many London dialects. Because it is non-standard, it should not be used in formal English. You, as a student of English, should never use it unless you really know what you're doing.
There's an old joke on this subject. A teacher knocks on the door of one of her pupils. The pupil answers the door.
Teacher: Hello. Are your parents in?
Pupil: They was in, but they is out now.
Teacher: "They was in"? "They is out"? Where's your grammar?
Pupil: Oh, she's in the living room, watching TV.