Yes we do believe in virgin birth of Jesus peace be upon him.
Mary pbuh was not an adulterer but given the honour by Allah Allmighty in the Holy Quran as the highest and the cleanest woman of all nations.
One and only G-d can create anything he wills without any reason.
In the universe we live ,there are some physical and (biological etc) rules established by Allah.
Prophet Adam pbuh is created without father or mother and without any example by Allmighty Allah.
Creation of Prophet Jesus pbuh is a clear miracle but this does not make him equal to God or son of G-d.
The miracle is that he is created without a father.
This is technologically possibble by cloning today. This does not make the miracle less important.
When a prophet helaed someone 2000 years ago , this is a miracle but many of those deseases can be healed by medicine today.
So creation of Adam is a much more bigger miracle if we look that way.
Holy Quran gives us a wonderful example to show the mistake here.
Peace