OK-
ish BNC lists it, but at no. 287 in the 'public +
<noun>' possibilities - more than 130 times less common than 'public sector' (the commonest in BNC - not in COCA though). See more here: corpus.byu.edu/bnc/x.asp?
Given the context, it would be possible to work out what 'public issue' signifies, but I think a native speaker would use more words - something like 'issue of popular/current concern'. Are you trying to do a word-for-word translation of two words in your native language, azhu?
'Agenda' comes from the Latin
agenda, meaning 'things that should be done'. In its concrete form an agenda is a list of things to be discussed at a meeting. However, 'agenda' can have a figurative meaning - 'things that
someone wants to do'. This explains the collocation 'public agenda': 'things that someone wants done, made public'. This is probably the usage your friend heard..
b