There is a statistical correlation between race (however conceived) and language, but it is not a perfect correlation. The overwhelming majority of people who learn Norwegian as their first language are Caucasian, and in fact live in Norway. The reason why the overwhelming majority of Norwegians are Caucasian (indeed, Norwegian) is because their parents were overwhelmingly Caucasian and Norwegian, ad infinitum. The imperfection of the correlation has many causes, but one is that a number of people moved into Norway from very different parts of the globe: but this is a relatively recent phenomenon (e.g. the Somali population in 1814 was close to zero, if not actually zero, but it is relatively large now). The best predictors of race and language are geography and history.
However, the fact that ancestoral Somalis do not know Somali, have no difficulty learning Norwegian (in Norway) or English (in the US) but do have difficulty learning Somali is evidence that ancestory does not convey an advantage in learning a particular language. There may be an appearance of an advantage in some cases, which comes from the fact of heritage languages and personal motivation, whereby 3rd generation Indians living in the US may know some Hindi or Tamil because their parents and grandparents continued speaking the language. But they still learn the local language, such as English, with absolutely no problems.
The correlation between writing system (e.g. logographic vs. syllabary vs. alphabetic, and which kinds) and race is even weaker, but still not totally unrelated to geography. For example, Cyrillic writing systems are limited to areas near Russia, which uses Cyrillic and is responsible for the practice of writing Mongolian in Cyrillic. The reason Japanese is written in kanji is that they picked up the habit from Chinese, and China is geographically adjacent to Japan. Writing habits are highly political, so that the single language Punjabi is written in two completely different scripts, depending on which country you are in.