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Insha Allah others can give more explanations as needed since I may not be able to answer all the things in detail, but there are two things that have to be kept in mind when examining the truth of Islam:

1. When we talk about religions like Christianity or Hinduism, we have to keep in mind that the Divine Being they claim to exist (that is, with the characteristics He has according to them) is a being that is impossible to exist. In the case of Catholics and Orthodox Christians for example, there cannot be a situation where a being incorporates within itself two mutually contradictory characteristics, which is basically what is claimed about Jesus and the Holy Ghost (that they are fully Divine in nature yet they also have total manifestations of their essence in the temporal world (hypo-stasis or whatever the term used by such religions may be)). This is nothing to do with us claiming that God is unable to do something or the other, but a recognition of what God is, and that His having certain attributes excludes their opposites.

Note that the Christians also hold on to this rule for certain things, which is why they argue with atheists about the Existence of God. This means the Christians understand that if "God Exists" is a true statement, then the statement "God does not exist" is false and should be opposed. It is not a matter of limiting God to human logic, but realizing that the question of the Existence of God is tied to reality and that reality operates in a certain way.

This is one of the principles that applies in this case. There is also of course the issue of how the narrations and legal reasoning of their founder has been passed down to us, but once someone knows that their theology is based on intrinsically impossible tenets, we know that the rest of the religion is founded on shaky foundations.

2. When it comes to sects like the Mutazila and the Khawarij, we would really like to know who are the Companions from whom such sects claim to have learned. There is a difference between having a group of dissenters and that dissenting group having a Companion who taught them their ways.

3. When it comes to the Twelver Shias, the matter with them is that they claim that the whole basis of the 12 Imams is so that the Muslim community can have the beliefs and legal reasonings coming from a perfect, infallible source, rather than scholars who can err. And this would be an issue to consider if their Last Imam was actually with them in person openly. But as it stands they are not in this situation and they have been forced to adopt our methodology (that of scholars approximating what the absolute truth is based on fallible methods). In the case of the Twelvers then, the chain of transmission should not even be there since they should be able to get everything directly from the Imam as per the logical foundation of their religion, but rather they have been forced to take our methodology even though the underpinning of their way should not allow for such a thing.