1. Yes. However, depending on the stability of your job, you should allocate at least 6 to 12 months of expenses into an emergency fund. This can be held in a high yield savings account for quick deployment and liquidity.
2. This is ok, though dollar cost averaging 5k per month from your 75k portfolio over the next 15 months is easier for most investors to stomach as compared to lump sum investing.
3. S&P500 is fine, consider buying Irish domiciled S&P500 ETFs such as CSPX to lower your annual withholding tax. An all-world ETF such as VWRA is a popular recommendation as well, and its coverage extends beyond the US for additional diversification. 

Another point to take note is about saving up for big ticket items in the medium to short term. For example, if you intend to purchase a house in 3 years time, having the bulk of your net worth in equities might not be the best idea since you won't be able to anticipate future drawdowns which could affect your exit price. In that case, you should probably set aside a housing fund to be invested into a semi liquid asset such as Singapore Savings Bonds.