Learn Turkish: Gerçekleri çarpıtıyor ve sadece bir unsuru vurguluyor. - He distorts the facts and emphasizes only one element.

This sentence just states two actions. How could we use our current lesson's asıl ... olan structure to emphasize the word unsur and say, "The actual element is the facts"?

You could say Asıl unsur olan gerçeklerdir. This applies the cleft-like emphasis from this lesson to firmly highlight that the facts are the core component being discussed, rather than whatever he is choosing to focus on.

Normally, an object modified by bir (a/an) doesn't take the accusative case marker. Why does bir unsuru end with the accusative -u here?

When bir acts as a generic "a/an", the object is indefinite and takes no suffix. However, because of sadece (only), bir here specifically means the number "one." He isn't emphasizing "an element" in general; he is singling out the one specific element. Therefore, it requires the specific direct object (accusative) marker.

The verb çarpıtıyor comes from the root çarpmak (to hit or to crash). What is the grammatical function of the -ıt suffix here?

The -ıt is a causative suffix. It changes çarpmak (to hit or to become warped) into çarpıtmak (to cause to warp, or to twist). In this context, it is used figuratively to mean twisting or "distorting" the facts.

How could we combine these two actions into a single fluid sentence without using the word ve (and)?