Yes, but it varied quite a bit depending on region. In northern Italy, for example, the cathedrals served their communities in a number of ways. Since the beginning of the 10th century, bishops began to occupy important roles in society. They often kept their own records. In Genoa, the earliest independent codification of "laws" was a rule of the See of San Lorenzo. Bishops often kept their own records and were important agents in the sale of grain, wine, and other staples and may have even dealt in slaves if the opportunity presented itself. All of this besides their primary role, to act as ritual centers for the citizenry.

This is all really vague. I can go into some of these elements further, or provide further reading.

For the first part, as has already been answered, yes. I would add to Enrico's list: cathedral complexes were the site of schools, of libraries and the episcopal archive, and a locus for the manifold ways in which power was publicly expressed in the middle ages.

Cathedrals took a long time to construct (some longer than others) for a great variety of reasons---labor, unrest, war, politics, finances. This is not a purely medieval phenomenon. The cathedral of St. John the Divine in NYC (often called St. John the Unfinished) has been under construction since the first decade of the 20th century.

The effectiveness of alms is going to vary vastly based on when and where your're talking about, as well as who is receiving the alms. But generally speaking, we don't have access to such detail on the daily lives of the peasantry, particularly such extremely poor members.

You might be interested in Maureen Miller's The Bishop's Palace as a place for further reading.