What is the ruling on continuing a relationship with a friend who holds affection and respect for you, while you do not reciprocate the same feeling, and harbor in your heart aversion and displeasure towards some of his actions, and feel hypocritical in showing him respect?

What you have mentioned contains no Sharia prohibition. Concealing one's aversion to someone is not deception; rather, it is a form of mudara (conciliation), which is among the best of manners. Imam Al-Bukhari titled a chapter in his Sahih: "Chapter: Conciliation with People," and thereunder he cited the saying of Abu Ad-Darda (may Allah be pleased with him): "Indeed, we smile in the faces of some people, while our hearts curse them." And from Aisha (may Allah be pleased with her) that the Prophet (peace and blessings of Allah be upon him) softened his speech towards a man whom he described as "the worst son of his tribe," and he said to Aisha: "Indeed, the worst people in rank before Allah are those whom people abandon - or leave - fearing their indecency." Ibn Al-Athir said: Mudara is to be gentle with people, to be a good companion to them, and to tolerate them, so that they may not shun you.