Working from home in Singapore

Before asking any such questions, first and foremost tell us what’s your current status in Singapore? Are you a foreigner holding any kind of WP? If yes, then working from home for any other work or for any other employer is illegal. You can only work for an employer who hires you.

Home office? Each company must have registered with registration number. And, work nature must have defined along with office address before seeking for registration.

As your questions are with half information, it’s hard to understand what’s your motive or intentions.

I managed my small business (actually, only me as freelancer) from home for a while (I was PR and thus allowed to do so).
If you work for a Singapore employer, ask the company for help with this. If not, register a business with ACRA. If you are allowed by your landlord to work in the property (get it in writing!) and the Condo rules also permit it (in case of HDB flats, you need to apply for permission from HDB), you can use your residence for the business. If not, you need to rent an office (shared spaces are pretty affordable!).