Hi! I'm a fresh grad with $13,000 in savings in my POSB Savings. How much would you recommend me to transfer to CIMB, and what should I do with the rest?

I would recommend you to set aside about 6 months worth of expenses in a high interest yield savings account. If you are below 26, Jumpstart account would be great! It offers 2% p.a. for your first 20k.

After you have set aside about 6 months worth of expenses I would suggest you to invest the rest!

I would recommend investing 50% in a market portfolio like S&P500 ETF as it historically yields 10% return and has a general upward trend. Another 50% can be other individual stocks that you like and see a potential of 10% return. Diversification is always important. There is no reward for bearing unnecessary risks. 

Accumulate once every 3 months and put it into a S&P 500 ETF quarterly! The historical returns are 10% and I would say it is much better than saving bonds​​

Yes it's possible, but do some simple calculations on your end. How much are you able to save in a month/year, take an annual growth of 5-6% (pretty safe gauge if you were to invest in a well-diversified portfolio) and see how long you will take to reach 100k.

CIMB will be good to keep your emergency fund. As a rule of thumb you should aim to keep at least 6-12 months of cash in your emergency fund.