You may have issues on several fronts. First, you don't even know if you will be granted the right to marry and obtain a long term visit pass (LTVP) to even stay in Singapore. See this ICA page:
http://www.ica.gov.sg/page.aspx?pageid=541
Second, in order to be able to work, you would need not a LTVP but a LTVP+. It used to be that you had to be married at least a couple of years before the LTVP+ would be granted, although the ICA website is silent on this matter now. See
http://www.ica.gov.sg/page.aspx?pageid=175&secid=171 You will need to verify with ICA.
Third, most residential leases prohibit commercial activity. It is one thing to be working inside your home with a computer or some other activity which does not generate foot traffic, and quite another to have people coming to your house all day long. I would be pissed if someone were running that kind of business out of their house in my neighborhood.
And finally, in order to work, you would need to form a business or a company then apply for a Letter of Consent (LOC) to work. See the threads in the Careers section for more information on forming a business and the LOC. Your problem, though, is that the business you propose is one that is/was not permitted for foreigners to start. Before they tightened up Entrepass rules, and just about anyone could start any kind of business, nail and hair salons were specifically excluded from the list of acceptable businesses, as well as massage, karaoke, and other similar. Thus, I believe you will have a very tough time getting LOC approval for your type of business, especially as you intend to do it from your house.
