They are not synonyms. An offering is a physical thing that you give away. On the other hand, a courtesy is an act (usually free) that is done out of respect, gratitude, politeness, or simple kindness.

No, courtesy is an act of kindness or a practice of decent and specially polite behaviour - probably from a person of a higher social status towards those of a lower one offering is a tangible thing you give to someone.

An offering is "something that is produced for other people to use, watch, enjoy etc." or "something that is given to a god as part of religious worship". Courtesy means "polite behaviour that shows respect for other people".

No