A Singaporean In Australia

I think you have a long way to go.

First, you need to know the differences among the wide range of visas that exist. I'll simplify them into 4 categories, namely, 

1) Visitor (tourist) visa

2) Student visa

3) Work visa

4) Permanent visa

Each type of visas have various subclass within them but you don't have to worry about this at this stage. Your questions about my situation will be answered after I explain these categories. A visitor visa is what Singaporeans apply for when they come to Australia for a holiday. This visa typically allows a 30 days stay like you mentioned, extendable by a good 60 more days or so on case by case basis. While visitors on business trips also come through under this visa, it does not grant the visa holder the eligibility to find employment. Those who do so are what we call the "plane jumpers" aka illegal workers.

A student visa as its name implies refers to a visa granted to a student who has applied to undergo a study program in an education institute in Australia. It grants the student the eligibility to work for not more than 20 hours per week during their school term and unlimited hours during school holidays. A bridging visa can be applied upon graduation that allows the student to find employment in Australia within a few months (depending on the type of bridging visa). If a student is unable to gain employment by the time his or her bridging visa expires, he or she will have to leave the country unless a different visa can be obtained.

The work visa is sponsored by an employer for a chosen candidate so that he or she can legally work in Australia. It is grants unlimited stay in Australia until the employer decides to cease the working relationship.

A permanent visa grants a holder unlimited stay or travel, renewable after 5 years, subjected to conditions. There are many types of permanent visas with different range of requirements. In general, most Singaporeans living outside Australia apply for Subclass 189 or 190.

If you manage to get yourself a Permanent Visa, you are eligible to run a business as well. If you plan to come to Australia via a business visa, the answer is 'No', unless you are already running a profitable F&B business in Singapore.

Yes, if parents are Permanent Residents.

We applied for Permanent Residence before we got married. So the short answer is 'No,' which is the same as the summary of the long answer.