Is one sinful for abandoning speaking eloquent Arabic and speaking in a prevalent vernacular — with its foreign words included — to avoid people's ridicule? And is that considered a weakness that hinders serving Islam and seeking Islamic knowledge?

It is not obligatory to speak in Classical Arabic (Fusha), and there is no sin upon one who speaks in other languages or common dialects. However, it is obligatory to learn Arabic to understand the essential matters of religion. There is no room for feelings of defeatism; rather, live your life naturally and strive to learn the language to understand the Qur'an and the Sunnah. Speaking in Fusha is good but not obligatory. If people mock those who speak it, they should be warned and advised. Do not belittle yourself; rather, have a good opinion of your Lord and strive to supplicate to Him that He may use you in supporting Islam.