Learn Spanish (Latin America): Ella tiene su propio negocio.

Not quite. While un negocio suyo translates to 'a business of hers', it doesn't have the emphatic meaning of 'her own'. To emphasize ownership in Spanish, you use the adjective propio right after the standard short possessive, as we see here with su propio negocio.

Why is propio placed before the noun instead of after it?

While most descriptive adjectives in Spanish go after the noun, propio is an exception when it means 'own'. It acts as an intensifier for the possessive adjective (su), so it naturally sits right between su and the noun.

If the sentence is about a woman (Ella), shouldn't it be propia?

No, because Spanish adjectives always agree with the noun they describe, not the person who owns it! Propio is masculine and singular here because it must match negocio. If she had her own company, it would change to match the feminine noun: su propia empresa.

Is negocio a false friend? It looks a lot like the English word negotiation.