"Married men study in Kollel...unmarried men study in a Yeshiva...several Yeshivot have their own Kollel. However, typically, married students, study together. They don't usually study with unmarried students."
What do they do for food, clothing, shelter?
At the Kollel (some but not all), the student receives a small monthly stipend. In my nephews case, he was married about a month ago. His wife, a terrific girl, was adamant that she wanted my nephew to continue studying. She is an English teacher and was adamant that she was going to provide for the family.
She resolutely from an early age apparently, told her parents that she wanted to marry a "talmid chacham" a Torah scholar. It was my nephews's intention after his Rabbinic studies to attend Yeshiva University in NY. He had been accepted into their Physics program (he's no nudnik!).
His wife, bless her, nixed that. She wants him to study.
Of course, this is not necessarily a typical situation but it is also not unusual. There are many families that live hand to mouth. However, it is their belief that Torah study is of paramount importance and that is how they choose to live. There are many charitable organizations that try to help these folks. To those organizations it is a labor of love. The fact that they can help facilitate the learning of a "chacham" (a learned man) is in itself a "mitzvah", a good deed. They also do qualify for government assistance, which is the source of much controversy in Israel.
Sorry for the long post, but it's important that we realize that orthodox families are not "sponges" soaking up government largess. Are there some that do? Unfortunately, yes. And that is a source of great embarrassment to the Orthodox community. They majority study because of their love of Torah. It is what we are commanded to do.
And thank G-d that they do study because it is they that have built the Jewish nation out of the ashes of the Holocaust.