Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
For details of about Tabligh group please read the Fatawa 85078 and 83288. On the other hand calling to Islam is not an individual obligation on every Muslim. It is a communal obligation. So, if some Muslims carry it out the others are exempted. As for specifying a given number of days for this noble mission (3 days, 3 months …etc) it is lawful if the objective behind it is to prepare the work better and organize it in a good way provided this period can be increased or decreased for any reason. But if this specified period has to be respected like a law, then this is an innovation as there is no evidence for it.
As for participating in shirk, innovation and other bad deeds, this is totally prohibited and we do not think that the Tablighi group indulges in such obnoxious deeds. But not denying such bad deeds can be for a good and valid purpose if the sinful person respects the Tawhid related matters. Then one can preach the sinful people in a progressive way (step by step) if there is real necessity for doing so. One should start with the most important. The evidence for this is the Hadith of Muaz. Muslim reported that Allah's Apostle said to Muadh bin Jabal when he sent him to Yemen, "You will come to the people of Scripture, and when you reach them, invite them to testify that none has the right to be worshipped except Allah and that Muhammad is His Apostle. And if they obey you in that, then tell them that Allah has enjoined on them five prayers to be performed every day and night" .
But if it is only for the purpose of not denying the Haram, then this is forbidden.
Allah knows best