1) The phrase seems slightly wrong, could it be "people in relationships"? That usually means people who are dating, but it can also mean family relationships, or work relationships.
2) Paraphrased... "In the corporate world, the best places to look, if you want to find new business opportunities, is among your former coworkers".
3) Paraphrased... "a character which appears often (in a play, novel, television show), and who has an important function in the story".
For example, if you had a drama on television about a husband and wife then BOTH those characters would be consistent because they appear consistently in every episode, and they would BOTH have a major function to the story, or theme. The "theme" of the story is similar to the subject of the story. A delivery man who appears in one episode and doesn't say anything would not be a consistent character, and would probably not have a "major thematic function" in a television drama.
4) Paraphrased... "here is a normal English family, they are close to each other and have good relationships".
Conventional in this context means normal, and in accordance with what everyone agrees is proper. A husband and wife with children is a conventional family. A wife with three husbands and an adopted chimpanzee that they call son, is an unconventional family.