I see that you've cherry picked propaganda that aligns to your presumptions about an entire group of people that you don't know or care to substantially learn about. Do you know what logical fallacy is?
I'd like to address these pieces individually.
1) yes. Islam does base the legitimacy of its source on circular reasoning. In fact, all of the Abrahamic religions do, at surface level. Apologists have found alternative justifications for the legitimacy of one or another. These justifications are, often, applicable to the sibling religions.
2) this is where the source runs into a problems. Their agenda is to discredit Islam, above all. The first problem is within the implications of their statements. There are many verses in the Bible that correlate to the most substantial violent parts of the Quran. If you condemn one, the other must be condemned for the same. The second problem is the logic. The source denied that the nonviolent ones are ideologically different. It's a false assumption