προσδοκίας [1 verse]( noun sg fem gen ) "For looking after" is prosdokia, which means "looking for" and "expectation".

Προσέχετε [9 verses](2nd pl pres imperat act) "Beware" is the Greek prosecho, which means "hold to", "to offer", "turn to or toward," "to turn your mind toward," "to be on one's guard against", "to take heed", "to pay attention", "to devote oneself to", "to attach oneself", "to continue", "to hold fast to [a thing]," "to have in addition," or "pay court to." -- The word translated as "take heeds" means"hold to", "offer", "turn toward", "attend to", "pay attention," and "be on your guard against". Its root is the Greek word meaning "have" and "hold". It works somewhat like our phrase "hold fast". It is a command to the group of listeners.

προσήλυτον, [1 verse](adj sg masc acc) "Proselyte" is  proselytos, which means "one that has arrived at a place," "sojourner," "a newcomer," and, from the NT use, "convert," "proselyte," and "one who has come from the Gentiles to become a Jew."  - (UW) The Greek word translated as "proselyte," isn't really translated since this is the Greek word itself. In Greek, the word means "newcomer," but it is used to refer to a person newly converted to a set of beliefs.

προσήλυτον, [1 verse](adj sg masc acc) "Proselyte" is  proselytos, which means "one that has arrived at a place," "sojourner," "a newcomer," and, from the NT use, "convert," "proselyte," and "one who has come from the Gentiles to become a Jew."  - The word translated as "proselyte," translated as "convert" in the NIV, shows up in Greek the first time here. It was apparently a new idea in Jesus's era, appearing only in the NT (here and in Acts), and in a few early Christian writers. It is a form of the common verb meaning "showing up like."

προσελθὼν [6 verses](part sg aor act masc nom) "He came"  is from proserchomai, which means "come," "go to," "approach," "draw nigh," in hostile sense, "attack," "come in," "surrender," "capitulate," "come forward to speak," "appear before a tribunal or official," "apply oneself to," of things, "to be added," "come in (of revenue)" and :"have sexual intercourse." -- The word translated as "went" is a special form of the word commonly translated as "come." It has the sense of approaching someone in authority, so "come forward to speak."