Is a person's love of being liked by everyone, and their appeasement of them to avoid disputes, considered hypocrisy? And is boasting about one's religion and Islam, or about any deed done for the sake of Allah after its performance, considered hypocrisy or showing off, despite the intention of sincerity to Allah?

Fear of hypocrisy and showing off (riya') is, if moderate, a sign of faith and drives one to purify deeds and seek sincerity. Your eagerness to maintain a good relationship with your family is a noble trait, as long as it does not involve religious flattery. Pride in religion is desirable, as in the Almighty's saying: "Say, 'In the bounty of Allah and in His mercy - in that let them rejoice; it is better than what they accumulate.'" You should intend your deeds for the sake of Allah and increase your supplications while striving to conceal your actions as much as possible, for concealment is better unless there is a legitimate religious benefit in showing them.