Is it permissible to use worldly examples to facilitate understanding of matters pertaining to the Afterlife and the servant's relationship with God, such as likening the Imam and the congregants to a manager and his employees in a company, or likening one who misses Fajr prayer to an employee who is late for a meeting with his manager? And are these examples the same ones used by Ibn Taymiyyah and Ibn al-Qayyim?

It is permissible to use worldly parables to bring otherworldly matters closer, in order to enhance understanding and solidify meanings in the mind. The Companions and those who followed them used this method. The parables used do not fall under the prohibited forms of تشبيه (likening) and تمثيل (representation). Rather, they are a form of permissible "Qiyas al-Awla" (analogy of the preferable), which implies that the desired ruling is more deserving of being established than the mentioned image. Thus, imperfections are far removed from Allah, and perfection is attributed to Him preferentially, as in His saying: "And for Allah is the highest example." This is the methodology of the Qur'an and the predecessors (Salaf).