Brendan always said he only needed two things to be happy and healthy. friends and family.

Correct sentence- Brendan always said he only needed two things to be happy and healthy: friends and family.

A period is used to end a sentence, but a period after "happy and healthy" may suggest the sentence has ended without explanation. A colon is used instead when introducing an explanation, example, or list. This will maintain the sentence’s flow and clarify the direct connection between the statement and the mention of "friends and family."

Because he had recently moved to a new city Peterson was sometimes lonely.

Correct sentence- Because he had recently moved to a new city, Peterson was sometimes lonely.

Commas are used after introductory phrases or dependent clauses to separate them from the independent or main clause. The sentence contains a dependent clause ("Because he had recently moved to a new city"), which cannot stand alone as a complete sentence, and an independent clause ("Peterson was sometimes lonely"). A comma is appropriate after the dependent clause to connect these clauses. This comma signals that the dependent clause provides context or explanation for the main clause.

San Deigo is suffering from a major drought; umbrellas are a common sight in the rainy city of Chicago.

Correct sentence- San Deigo is suffering from a major drought. Umbrellas are a common sight in the rainy city of Chicago.

There are two independent but illogically related clauses in this sentence. Droughts in California have little to do with umbrellas in London. Because these ideas are unrelated, they cannot be joined with a semicolon.