the ' is a breath mark. in this context, it's indicating a wind player to breathe at that moment. the same meaning applies to vocalists. it can also appear outside winds or vocalists. in such cases, it means to take a slight pause without necessarily altering tempo (usually by shortening the preceding note)
the > is an accent. it indicates to play with greater emphasis. how that emphasis comes through depends on the musical context, but it often means playing that note louder or stronger
I've always been taught that the accent is explicitly not to be treated as playing the note louder or stronger as whole, but rather to emphasize the beginning of the note by quieting the end of the note, i.e. treat the > as a note specific decrescendo
correct, but the part shown here is for a transposing instrument. it sounds a fifth lower than it is written. so though it is written as A and E, in concert pitch, these notes are actually D and A