Assalaamu alaykum. 1) Someone prays in a slow, moderate manner (he usually prays in this manner) and performs the sunnah acts of the prayer (raf'ul yadayn, jalsah istiraha) and wants to teach the other ignorant people who pray quickly and do not know the various sunnah acts of the prayer. Is this considered showing-off (riyaa')? 2) Someone found a small amount of money (5 taka, which is less than 0.5 KSA riyal) and gave it in charity without finding its owner. Is that permissible?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

Linguistically, the Arabic word riyaa' (ostentation or showing off) is derived from the noun "ru'yah", which means seeing or observation. So riyaa' means performing acts so that people would see them. Al-Qaraafi wrote, “Riyaa' means performing acts of obedience with the intention of winning people's praise and admiration.” [Az-Zakheerah] Al-Ghazaali wrote, “Riyaa' is to seek (the praise and admiration of) people when carrying out acts of obedience.” [Ihyaa' ʻUloom Al-Deen]

Based on these two definitions, it is clear that whoever performs the prayer before people in the manner described in the question with the purpose of teaching them or similar purposes that do not contradict the due ikhlaas (i.e. sincerely devoting the intention of acts of worship solely to Allaah), his act does not fall under the heading of riyaa’, especially if he usually performs the prayer in such a slow, moderate manner as you have stated in the question.

As for your second question, please refer to fatwa 84786.

Allaah knows best.