The question is a bit long. Let's look at the following supplementary question: My grandmother's consultation in Singapore.

Does your grandmother have no position in Singapore? If not, you will not be able to apply for permanent residence or citizenship in Singapore.

Your grandmother's relatives immigrated to Singapore and basically did not need the relationship between your grandfather and your grandmother.

Basically, you have to rely on yourself. Your grandmother's grandson wants to work in Singapore on his own.