Hi,

- At a hospital a receptionist  attends, sees or receives people?; The word 'receptionist' is derived from the word 'receieve', so it seems a bit repetitious. I'd say 'deals with', or maybe 'greets'..

- I appreciate the union of singers and public during music festivals. (is it correct to write the union in this context?); It sounds awkward. Perhaps you could talk about 'the connection between'. I'm not exactly sure what you mean.

- I saw the Carpenters show a long time ago.(is it correct to use the verb to see here?);  Yes.

- At the moment I 'm studying some information technology programs (what should I write it?); You study a subject (eg information technology). You do/take a course. I'd say you do a program.

- They need to work (or) they need working (?); Only the former.

- She wants playing (or) she wants to play (?); Only the latter.

- "Now what matters is that she's fine" (is there any grammar mistake in this sentence?); No. But I think it would be more common to say 'What matters now is . . . '

- What do we call someone that is a consumer in potential ? Is it called a great consumer ?; Say 'a potential consumer'. Such a person has not yet bought anything. Ehen they do, I'd call them 'a great customer' (if they buy a lot).

Best wishes, Clive