The answer to your first question is "Unlikely". This renders the next two questions moot.
Many countries have either a "remote worker/digital nomad" visa or "person of independent means/retirement" visa (or both).
It doesn't look like Singapore is one of them
Unfortunately, Singapore doesn't have a digital nomad visa at the time of writing. This means you need to either stay for up to 30 days as a tourist or apply for an actual visa to stay longer. For example, you might be able to apply for an EntrePass work pass, depending on the nature of your work. Or if you're a recent graduate, you can apply for a Work Holiday Visa, which will allow you to stay for up to six months if you're granted this visa.
No Retirement Visa for Expats
While many nations want to promote foreign retirees coming to their country, through the offerings of perk-based retirement visas, Singapore is exempt from this list. This does not make it impossible to retire to Singapore, but you’ll need to take a longer or more expensive route to achieving your leisurely dreams.
In order to relocate long-term to Singapore, you’ll need to acquire permanent residency in the country. This can be done in one of three main ways: Employment Pass, Global Investor Programme, or Foreign Artistic Talent permit.
The Employment Permit can be achieved through qualified hiring by a Singaporean company. Expats holding this Employment Pass can apply for permanent residency after one year of living abroad and working in Singapore. Once permanent residence is obtained in Singapore, an employment pass is no longer needed to maintain working legality in the nation. Permanent residency is valid for 5 years before needing to be renewed.
The Global Investor Program (GIP) allows expat investors to receive immediate permanent residency in the country. The minimum starting investment is $2.5 million SGD ($1.85 million USD). Applicants are given 6 months to complete investment from time of permit approval. Unmarried dependents and spouses can achieve permanent residency after the applicant’s GIP has been received. Parents of the PR holder can be added to the residency program for an additional investment price of around $220k USD per parent.
Foreign Artistic Talent allows for those with exceptional talent in the arts, photography, dance, literature, music, or film to receive permanent residency in Singapore. To qualify, applicants must demonstrate that they have made significant contributions to Singapore’s art scene.
Unfortunately, unless you are willing to make a large investment into a company in the country or work for the required years necessary in Singapore to receive permanent residency, you’re options are limited.