Q11: Is it obligatory for the individual to respond to fallacies posted on the internet especially if they were false accusations against Almighty Allah, the Messenger, the Ahlulbait (peace be upon him) or our noble scholars for the sake of decreasing the esteem of truth and its people?
There are no specific rules regarding the obligation of responding to fallacies posted on the internet, as it is at the same rules apply with regards to every fallacy against the truth and in any media.
There is no proof for the obligation to confront every fallacy and respond to it. The most that can be said is that the necessity to refute it depends on if it was strong enough to be difficult to answer and was so important that it is going to harm and weaken the religion. Since answering it would protect the religion, it is necessary to do so, as it is a kind of Jihad, which is Wajib Kifai (which refers to an obligation upon all aware Muslims but if some of them undertake it, the rest will no longer bear the religious responsibility(.
If it does not reach this level of importance, responding to it is a sort of propagation and service for the religion, and it is undoubtedly recommended, but it is not considered obligatory. The aforementioned details are about the necessity to explain and respond to fallacies initially even without being asked about it. It is so even if the truth is unknown to the individual if he could learn about it in order to explain it to others. However, if the individual was asked about a religious truth that he knows and there is no obstacle or embarrassment to explain it, then it should absolutely be explained, even if it was not very important, since it is prohibited to hide religious knowledge.
Q12: if the individual was asked about addresses to websites that may serve the religious interests of those who asked, such as saving them from committing sins and answering claimed fallacies, and he knows if they – especially this particular group of believers – were not answered, they would definitely be subject to sinning and the like. Can he neglect guiding them to the websites?
What appears to be the question is the request of a group of believers to learn how to reach websites on the internet that are beneficial to their religion, help responding to fallacies, explaining truths, reminding about Almighty Allah, approximating to Him and similar aims.
Apparently answering and guiding them is religiously much recommended to whoever can do so, as it is answering the need of a believer and especially this kind of need. It is feared that not explaining would lead to Allah’s abandonment of the individual who was asked because such is considered as belittling the response to the believer's need when he is able to do so.
It is obligatory to pass the requested information when it is feared that not doing so and leaving the believers in their ignorance would allow the spreader of falsehood to take advantage of them and misguide them, thus supporting falsehood in a way that harms the religion and weakens it.