yes it occurs naturally in the cells. many genes are regulated by RNAi. In mammals, miRNAs are predicted to control the activity of ~50% of all protein-coding genes. Functional studies indicate that miRNAs participate in the regulation of almost every cellular process investigated so far.

Yes it does; RNAi is a natural cellular means of regulating genes; it is considered to have evolved from an early defense mechanism against viruses. It recognizes double stranded RNA (dsRNA) as foreign to the cell, and destroys it along with mRNA, and other single stranded RNAs; such destruction leads to the post transcriptional inhibition of gene expression and of protein synthesis.

Refer to many publications by Shiv Grewal's Lab at NIH for multitude of examples and mechanistic insights. Yes - in short! 

mammals dont have siRNA, only miRNA. so its fine tuning of many protein levels, not elimination of one specific target