What evidence of culture do you see in your community? Example (For example, restaurants, festivals, clubs, organizations, etc.) Can culture be ‘given’ to a group rather than ‘created’ by a group? Example (For example, who decides the characteristics of a culture? The people themselves or those who observe/invade/conquer/oppress them?) Is it possible to belong to more than one culture or cultural group? Explain Example (For example, what of the “hyphenated” cultural groups such as Carib-Canadian, Chinese-Canadian, etc.) If someone belongs to more than one cultural group, how might they determine their primary culture? Example (For example, if you are of mixed heritage, do you define yourself with one group over another? How does one make that determination?)

Culture includes the social behaviors and norms established by a particular society. It also includes examples of intellectual achievement, particularly in the arts.
The first question is very personal and you must tailor it to what you see in your community. Restaurants are the most obvious examples of culture. Many communities have a variety of restaurants—Mexican, French, Italian—and even "standard American fare" includes the influences of other cultures. For example, hamburgers and hot dogs are a result of the German influence on cuisine. Family restaurants, such as The Olive Garden, are the result of the standardization of Italian cuisine.
The second question is more complicated and is debated frequently today in the context of cultural appropriation—that is, the habit of dominant cultures to use, or appropriate, the cultural products of other groups, and to profit or benefit off of them while excluding the people who invented those cultural products. There are multiple examples of this in American culture, including everything from hairstyles to music. A prominent example is the popularity of rap and hip-hop. When rap first emerged in the South Bronx in New York City in the late 1970s, it was not regarded favorably. The music was associated with lower-class black and Latino youth. However, when it became profitable, white musicians also released albums, contributing to the genre becoming more mainstream.
Something similar occurred with jazz after the First World War and with rock and roll in the 1950s. Record producers wanted to sell the music, which had mass appeal, to white youth but could not promote the black artists who created the music—hence, The Original Dixieland Jazz Band, whose leader Nick LaRocca, went so far as to say that black people had no influence on jazz, and Elvis who became the "King of Rock and Roll." Jazz, rock and roll, and rap are all products of American culture and are a reflection of the influences of different groups on cultural forms. Jazz, for example, was invented by black people in New Orleans, but it was influenced by both African and European musical traditions.
It is usually the dominant group which decides, through money and social influence, what the most viable cultural products are. However, it would be wrong to falsify history and say that Elvis invented rock and roll. He contributed to its popularization and brought his own ideas to the form, but he did not invent it.
It is absolutely possible to belong to more than one cultural group. Hyphenated identities are more common in places with histories of migration. The United States is an excellent example, for most of its citizens have origins elsewhere and their ancestors brought certain traditions and cultural histories with them when they immigrated. Thus, people are Irish-American, Chinese-American, or Lebanese-American, among many other identities. Black American, or African-American people, are unique in that their culture was formed as a result of slavery and segregation. A community was formed among people who were originally of very different groups. Some kidnapped people came from present-day Nigeria, which also has numerous tribes, while others were from present-day Senegal. These people spoke different languages and had different customs, but formed a new culture based on the shared experience of oppression in the New World.
"Primary culture," as you call it, is usually based on national identity. For example, a person of Algerian descent who was born and raised in France will probably have the hyphenated identity, "French-Algerian." However, that person is likely going to identify more as French, for it is the cultural norms (e.g., standards of behavior, food, systems of infrastructure) of France that they know and with which they would most likely identify.
France is a diverse country, but French identity is rather distinct. Though people's habits and politics may vary from region to region, there is a shared sense of history, a generally shared cuisine, and an understanding of manners. The same applies to British culture and identity. American culture is harder to pinpoint. Arguably, there is no distinct American culture. People in rural Montana live very differently from people in rural Mississippi. Even major cities, such as Los Angeles and New York, are very different from one another and the people have different habits and approaches to life. Culture is not always easily definable.