Learn Spanish (Spain): La mujer hace una encuesta y pregunta si conozco la marca. - The woman does a survey and asks if I know the brand.

In reported speech, you are stating that a question was asked rather than asking it directly, so you don't use question marks. The word si means 'if' or 'whether' in this context, which never takes an accent mark. The accented sí means 'yes'.

If the original question was about 'you', why is the reported verb conozco in the 'I' form?

When reporting speech, you have to change the perspective to match the new speaker. The woman originally asked 'Do you know the brand?' (¿Conoces la marca?). Since you are the one reporting what she asked you, 'you' becomes 'I', so the verb changes to the first-person form: conozco.

Does hace una encuesta mean she is taking the survey or conducting the survey?

Here, it means she is conducting or carrying out the survey. In Spanish, the phrase hacer una encuesta can mean both to conduct a survey (like the pollster in this sentence) or to take a survey (like the respondent), depending entirely on the context.

Why do we use conozco instead of sé for knowing a brand?

You use conocer when you are talking about being familiar with a person, place, or thing, such as a brand. You use saber for knowing facts, pieces of information, or how to do something. Since a brand is an entity you are familiar with, conozco is the correct choice here.