How complex it is to register a Limited Liability Company in Singapore

Singapore actively encourages new business setup and makes the process very easy. Registering a Limited Liability Company can be done online, takes just a few hours and costs just a few hundred dollar. You do need a locally resident manager, though. (And you cannot easily get a resident visa based on being shareholder.)
However, they are only interested in businesses that actually operate in the country and contribute to the local economy (e.g. by hiring local employees) - purely online or offshore businesses do not qualify.
Go to acra.gov.sg for more information.
There are also service providers (like Janus or Rikvin) who complete the formalities for you (for a fee) and can even supply locally resident directors and managers,

Opening a business bank account is a different story and depends on the bank you deal with, so inquire there.