Your sentences are correct. What you are saying is "that (person) is John". We just don't use the noun if it is obvious in context. Saying 'that is John' suggests that the person you are speaking to has already identified which man you are referring to. But if John was with a group of other men and you wanted to point him out you couldn't just say 'that is John' because the listener wouldn't know who you meant. So you would describe him - that (man over there with the beard) is John.

Thank you for your help!

//"That" seems as if I were indicating a thing rather than a person, don't it?// No, it isn't doing that. "That" is used for everything: person, animal or thing. Your examples are fine. Say it just like that. //don't it?// This is the wrong declension. I don't You (singular) don't He, she, it doesn't ***** USE THIS ONE --> It [the word "that"] seems...doesn't it? We don't You (plural) don't They don't. // as if I were indicating// This is a very good example of the rare subjunctive case in English. Nicely done. You are going better than far too many badly educated native English speakers. Keep learning. You are doing well.