Assalaamu alaykum. Is greeting any Muslim with the Salaam or supplicating for them when we want a favor from them a kind of showing off?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

Greeting Muslims with the Salaam or supplicating Allah in their favor is not a kind of showing off (Riyaa'); rather, it is an act of the Sunnah encouraged by the Shariah and is pleasant to human nature. ʻAbdullah ibn ʻAmr reported that a man asked the Prophet, sallallaahu ‘alayhi wa sallam, "Which act is the best in Islam?" He replied, "To feed (people) and to greet those whom you know and those whom you do not know." [Al-Bukhaari and Muslim]

Abu Umaamah narrated that a man said to the Prophet, sallallaahu ‘alayhi wa sallam, "O Messenger of Allah, when two men meet, who should greet the other first?" He replied, "The one closest to Allah." [At-Tirmithi and others]

Greeting with Salaam is one of the means of getting to know one another and fostering brotherly affection among people and a means to enter Paradise. The Prophet, sallallaahu ‘alayhi wa sallam, said, "You will not enter Paradise until you believe, and you shall not believe until you love one another. Shall I inform you of something, if you do it, you will love one another? Spread the greeting of Salaam among yourselves." [Muslim]

In addition, it is an act of the Sunnah to supplicate Allah for the person who you hope will do you something good or who has done you a favor. The Prophet, sallallaahu ‘alayhi wa sallam, said, "If anyone does you a favor, reward him. If you do not have the means to reward him, supplicate Allah in his favor until you feel that you have rewarded him." [Abu Daawood and others]

The Prophet, sallallaahu ‘alayhi wa sallam, also said, "Whoever receives a favor and says to the person who did him this favor, 'Jazaaka Allah khairan' (may Allah reward you), has expressed gratitude to him as due." [At-Tirmithi, An-Nasaa'i, and others]

As for showing off, it means doing something so that people would see you doing it. It is contrary to sincerity (Ikhlaas), which is doing good deeds solely seeking the pleasure and reward of Allah.

Allah knows best.