To touch on your third question: "Did converts face any social repercussions?"

This is definitely an interesting question! This is actually something that Dijana Pinjuh tackles in their relatively recent Conversions to Islam in Bosnia and Herzegovina, and the Connections between Converts and their Christian families, from the Ottoman Conquest to the End of the Seventeenth Century. Quite a mouthful of a title! But, nonetheless, they do a really revealing dive into what life was like for Christian converts to Islam in this region.

Therefore, I will first touch on their points and then explore their ideas through other current academics, such as Ines Asčerić-Todd (see Dervishes and Islam in Bosnia: Sufi Dimensions to the Formation of Bosnian Muslim Society) and Tijana Krstić (see Contested Conversions to Islam: Narratives of Religious Change in the Early Modern Ottoman Empire), who have both examined similar questions in Ottoman Bosnia.

Pinjuh moves away from the slightly older theory that Muslims and Christians failed to co-exist. This is often called the "clash of civilizations" narrative, in which Islam and Christianity are portrayed as in an eternal battle with one another. Instead, Pinjuh explores Ottoman census and court records, which show a rather different story. In fact, they argue that formerly-Christian Muslims and Christians lived mostly harmoniously.

Their first major point is that Christians continued to live together in the same house, even if one of them converted to Islam. This is shown through Ottoman census records, that record the religions of each person in a household. Oftentimes, in these records, we see mixed families, in which some people had converted to Islam and others had remained Christian. Therefore, many converts do not appear to have been shunned by their Christian families.

Their second major point is that Muslims and Christians jointly held property and land together. Fields, vineyards, mills, and other agricultural lands are evidenced as having been shared between brothers that were Christian and Muslim. So not only did Muslims and Christians often live together, but they often worked together.

Their third major point is that inheritance rights were protected regardless of religion. In fact, inheritance disputes, that are recorded in the Ottoman courts, between members of different religions rarely mention religion as the reason for the dispute. And through Ottoman census records, we find that Muslims often did inherit lands or properties that were formerly owned by Christians.

While these three points are rather straight-forward, since we have rather clear evidence of their existence, we now enter a bit of a convoluted mess: the issue of whether Bosnian and Herzegovinian were sincere in the conversion to Islam or if they had somehow become "false" Muslims.

If they were not sincere, you could see how one could argue that the aforementioned points are rather moot, for such converts were not "truly' Muslims. To understand this better, we need to understand the more recent debate of syncretism.

Our best exploration of the syncreticism debates comes from Krstić's Contested Conversions to Islam: Narratives of Religious Change in the Early Modern Ottoman Empire, which presents several different theories of the debate and argues that a new framework for understanding Christian conversion to Islam in Bosnia and Herzegovina must be established. While some have argued that many converts were not "true" Muslims, Krstić posits that such arguments fail to account for the natural flexibility in Islamic belief.

This syncretism, some have argued, allowed Islam in Bosnia and other regions of the Balkans to flourish. For Islam was not seen as an entirely foreign faith, but one that was inherently intertwined with Christianity. Even some aspects of Islam were altered to be more appealing to potential Christian converts. Such an example of this was the raising of Jesus' prominence in the Islamic faith in Bosnia and Herzegovina. So while Islam was different, it appeared not entirely unknown and, in some cases, even appeared familiar.

Therefore, it is possible that this may account partially for the seemingly co-existent nature between Muslims and Christians in the region.

Nonetheless, the relationship between Muslims and Christians in the region is complicated and there are certainly many competing theories on how to interpret this information. However, the evidence from the Ottoman census and court records are hard to deny for someone that would want to argue that they didn't co-exist in a mostly peaceful fashion. And while one could argue that they were Muslims only in name, this neglects the flexible nature of Islam and fails to account for the naturally syncretic nature of two culture and faiths interacting.

Bibliography

Pinjuh's Conversions to Islam in Bosnia and Herzegovina, and the Connections between Converts and their Christian families, from the Ottoman Conquest to the End of the Seventeenth Century. This entire article is really fantastic for this question.

Asčerić-Todd's Dervishes and Islam in Bosnia: Sufi Dimensions to the Formation of Bosnian Muslim Society, see page 5-6.

Krstić's Contested Conversions to Islam: Narratives of Religious Change in the Early Modern Ottoman Empire, see "Introduction", section "'Syncretism,' 'Toleration,' and Conversion in the Historiography on the Ottoman Empire"

The banate of Bosnia was officially Catholic, and consecrated its bishops in Catholic Ragusa (modern Dubrovnik), but used Old Church Slavonic in its liturgy. As for the actual church ‘on the ground’, there was a so-called Bosnian church, which was widely popular among the populace, but it seems to have been deemed heretical by both the Orthodox and the Catholics, and placed under an Inquisition by the Western church, and was previously linked to the Bogomils rather than Orthodox (though this doesn’t seem to reflect their actual beliefs). The exact details of why it was seen as heretical by Rome and Constantinople and others are still not entirely clear, but there are some interpretations and analyses by Horak here and by Fine here. In the late 13th century they were eventually put under an Inquisition with the approval of Rome.

Eastern Orthodoxy had a foothold in parts of Herzegovina nearer Serbia.

There were also Bogomils, whose dualist philosophy (generally deemed as heretical and akin to the Gnostics or Cathars) originated in the Bulgarian Empire (in what is now Macedonia) and spread to an extent around the Southern Slavs. For a long time the Bogomils and Bosnian Church were seen as linked, but this now seems to be questionable.

This split ‘boundary’ status - having a de facto compromise church that neither most Orthodox nor Catholic authorities approved of - made Bosnian Christianity particularly vulnerable when the Ottomans invaded. The Ottomans favoured the Orthodox churches and allowed Chalcedonian East Orthodoxy to grow there, given that Constantinople and Serbia were already under their sway (while Catholics were under the sway of an outside enemy papal power). But of course Islam was favoured even more, and since most Bosnian Christians didn’t have the influence of a major power, or a century or two into Ottoman rule even well-versed and trained priests, but rather more corrupt and uneducated substitutes, the hold of Christianity weakened. Islam, however, offered a chance of power in the Ottoman regime (several prominent viziers were of Bosnian extraction), and allowed for them to escape the jizya (a special tax on Christians and Jews) and devshirme (the practice of enslaving millions of non-Muslim subjects’ boys for use as janissaries). So without a more compelling and well-connected alternative, Islam took over.