Muslims built the mosques on the lands, by the choice and acceptance of the people of these lands, where people required these mosques to practice their Islamic religion rituals. Muslims victory was neither on the lands nor on the civilian people who are having these lands. This victory was either on the disbelievers who attacked Muslims or on the tyrants who where oppressing their people and were not allowing them the free choice of selecting their faith. A good example is the migration, in secrecy, of Jesus (Isa in Arabic) with his mother Mary (Mariam in Arabic) from the currently called the Palestinian Territories to Egypt to escape the tyranny of the Romes against the Christians.
The Koran (018:021) states: 'Build a building over them, their Lord knows best about them;' and
those who prevailed in their affair said, 'We will surely make a mosque over them.'
This is not a direct commandment to build on a place of victory, but there is a tradition of building mosques to celebrate or symbolize victory.
"The al Aqsa Mosque in Jerusalem is built on top of one of the holiest sites in Judaism, the Temple Mount. The former St. Sophia's Basilica, once the world's largest cathedral and orthodox patriarchal basilica, was torn down and replaced with the principal mosque of Istanbul. The Cordoba mosque in Spain was a former Christian cathedral. Muslims have engaged in this practice for centuries, symbolizing their victories over the infidels."
I have seen this verse from the Koran quoted many times and decided to research it. This verse has been claimed to be taken out of context, but saying that something is "taken out of context" is part of the Islamic practice of "Taqiyya" which is inspired by the example of Mohamed, praised in the Hadiths as "the greatest deceiver". Taqiyya is religiously sanctioned lying, deception and tactical dissimulation. It can take the form of lying, talking in circles, playing the victim, false claims of torture, blaming others for evil acts, saying Islam forbids that, carrying signs that say 'Peace', saying the meaning was TAKEN OUT OF CONTEXT or lost in translation and claiming that Islam has been hijacked. Taqiyya is used to fend off criticism of Islam and/or Muslims.
The passage in the Koran is about the Seven Sleepers (aka People of the Cave in Islam) who were persecuted by the Romans for their belief in God. It is not an actual story about Muslims or Islam but a story recounted by the Muslim's prophet Mohammad (PBUH) to the Muslim people. (kinda like a biblical story).
The Quran verse is:
{
We caused them to be discovered, to let everyone know that GOD's promise is true, and to remove all doubt concerning the end of the world. The people then disputed among themselves regarding them. Some said, "Let us build a building around them." Their Lord is the best knower about them. Those who prevailed said, "We will build a place of worship around them."}
"We" , in the verse, does not refer to Muslims as this story is about an event pre-Islam. The verse also describes what the people of that time (again pre-Islam) wanted to do with the 7 sleepers in Ephesus.
There are many stories in the Koran, about Adam, Mary, Noah, Moses, etc...further research is always required for a more complete understanding.
And the answer to the question is yes and no. The birthplace of Islam, Judaism and Christianity is in the Middle East. They were all empires that grew and conquered territories to spread their message - hence the prevalence of Christianity in the Americas. And places of worship were commonly built next to or on top of others. The Omayyad mosque in Damascus, Syria was a church and before that it was a temple to Jupiter in the Roman era and before that a temple to Hadad in the Aramaic era. Btw, St Sophie's was not torn down, it became a mosque and is currently a museum.
Answer B and the comment on it, that is given in C, is an example of the many falsified arguments used by some people, intentionally or unintentionally, to attack Islam and their holy book Quran. They extract from Quran a word or part of a sentence to defend their false claims against Islam but when you look to the full Quran text you can easily verify the falsification of their claims.