Is my feeling that people are looking at me when I pray, and my imagining reciting the Qur'an in front of them, and my asking questions in scholarly gatherings, and my delight in people's praise of me, and my desire to appear as an intellectual when speaking about religious information, considered showing off (riya') or a satanic whisper (waswas)? And how can I get rid of that?

These are whispers (waswas) that should not prevent you from doing good and worshipping. Do not abandon good deeds for fear of showing off (riya'), but rather strive for sincerity and perform righteous acts, and do not respond to Satan's distractions. Ibn Taymiyyah said that whoever has a prescribed regular devotion should not abandon it merely because people are present, as long as his intention is for God. Al-Fudayl ibn Iyad said: "Abandoning an action for the sake of people is showing off (riya'), and performing an action for the sake of people is polytheism (shirk (definition))." Let your joy be in being granted success in obedience, and focus on God's praise and commendation. Furthermore, any friendly relationship between a man and a woman must be cut off as a precaution against evil and temptation.