I can't speak in regards to Khan Academy's effectiveness since I've never seen one of their videos on history, I can answer your secondary question.

In my opinion the best way to "get better" at history is to simply read well-written and well-received academic history works. Pick a time period or a location or topic that interests you, and do a bit of research to find some seminal works on the topic. Then read them rigorously. Observe how writers interpret sources, present viewpoints, build on top of existing historiography, and make a new and original argument. Besides, if you're interested in that topic, as a history major you'll be expected to know or eventually know the most well-known works on the topic.

I did my undergraduate history thesis not my final semester, but my second to last semester in school. While I was decent at writing history papers before, the sheer amount of reading and research I did for the thesis propelled me much further, and for my classes the next and final semester (at one of the highest ranked undergraduate history programs), I was cranking out A+ papers in 5 hours with minimal proofreading.

I watched the entirety of the "world history crash course" videos. At approximately 10 minutes per topic (forget total runtime - 4 to 6 hours or so) they provide at best a general overview. For example the Mongols and Genghis Kahn are covered in about 10 minutes.. I think that alone shows how in depth these are (not very)

IIRC the rest of the videos mostly cover more recent history (American civil war, WW1/2, etc) in slightly more detail.

As a rule of thumb anything on Kahn academy is reviewed by scholars , however because their goal is to keep videos short and to the point you will always sacrifice some of the detail and nuance