You can run a salon from a residential property, as long as it’s primary use is a residence. Just like you can run any legal business from a home office. It is NOT illegal.
What is illegal is to have a house in a residential zoned area, and operate any business from that, without it being your primary place of residence. I don’t know requirements of strata complex
You would have to have it registered with the local council for compliance to health regulations. Some councils perform annual inspections, others just do surprise inspections. Most require an annual re-registration. They will also as for certficate of currency for business insurance etc.