Which is better and more correct for the mosque preacher and teacher when reminding people of something previously mentioned: Should he say "I previously mentioned or said" (using the singular form), or "we previously mentioned or said" (using the plural form), and does the latter phrasing imply self-praise?

Both phrases are permissible. However, it is preferable to use the singular pronoun out of humility. There is no harm in attributing the statement to yourself to remind people of it, as long as you do not intend pride or superiority. You can avoid both expressions by saying, "as previously explained" or "it was mentioned earlier."