Is uploading videos and pictures to Facebook that feature luxurious cars, or renting luxurious cars for an occasion, considered showing off to people? And what are examples of showing off?

Fabrication (Tasannu’) is the feigning of righteousness and displaying good conduct contrary to one's inner state. What is mentioned in the question is not among the blameworthy forms of fabrication, unless it deceives people into believing one possesses what they do not, in which case it might be considered like "satiating oneself with what one has not been given." As for Imam Al-Ghazali, he holds that riya’ (ostentation)—which is seeking status—if it is outside the realm of acts of worship, has a detailed ruling: it may be permissible, an act of obedience, or blameworthy, depending on the purpose. Seeking a small amount of status for a need is commendable, while seeking a great deal may distract and lead to transgression, but it is not unlawful unless it leads to engaging in prohibitions. However, the preoccupation of one's concern with it is a starting point for evils.