The rules on English aristocracy dictate that only the title holder is technically noble. So the Duke of Marlborough for example is a nobleman, but his wife the Duchess is not, she is given an honorary title. The same applies to his sons and daughters; only the office holder is permitted to be a noble person. As a result, in England if you have to ask if you're noble, you're not. (There are slightly different rules and titles in Scotland, Wales [I think] and Ireland I'm not qualified to comment on.)

However, this is different from the Bourbon French idea of aristocracy which ennobled all members of a family. This came into conflict as well with the ideas of inheritance in that all members of a French noble person's family would receive an equal share. As a result, I can't accurately comment on the number of noble French people living today where you can identify with great accuracy the number of noble English.

Source: Debretts Handbook, 2016.

It really depends on the style of nobility, the legal standing of the class, and the type and strength of government at the time. In France, before 1848, the nobility was granted a few special legal rights by the monarchy. Nobility could be lost if engaging in a profession that was considered common labor. It was a hereditary right, passed along to legitimate male heirs, and also by marriage if the man was noble. Thus, a daughter could not marry a commoner and remain noble, and so would probably be encouraged to marry a nobleman. This social class structure would encourage courtship and marriage amongst nobles, and so nobility would not expand to the commoners very quickly. The monarchy was generally strong in France, and had reason to limit the power of the nobility, and the noble class was never very large.

In contrast, the Polish had a very strong noble class (Szlachta) that removed the hereditary monarchy, and had very broad rights and privileges. The philosophy of the nobility was that all members were socially equal, despite vastly differing wealth, professions, and political clout. A good part of the nobility was also probably made up of pretenders with no actual claim to nobility. At its height, in the early 18th century, it's estimated that the Szlachta made up 15% of the population.

Most nobility is directly hereditary by design, to function as a stable upper class, but that doesn't mean that every single family member or descendant is a member of the nobility.

Are we allowed to ask related questions here? I'm curious as to what kind of jobs family members of nobles would be able to acquire. If you were the son of the Count's brother, say, what sort of positions would be available to you?