How much to invest per month? 10% per month?

It depends on your salary, minus off your expenses, insurances, etc. Then whatever left over that you save inside your bank account, use a portion for investment. The amount to use for investment depends on individual preference. But I suggest to save up more fo remergency fund before you even start investment.

Up to you

If you are Singaporean and PR, the extra 17% is a life saver.

CPF forced savings, so if you can squeeze 20 -30% take home pay and invest it, will be way better.

How much to invest per month depending on how much you can allocate to each month. In principle, divide your income into few buckets starting with first bucket for long term investment (generally, 15 20% for most), then 2nd bucket of around 30% for daily expenses, 3rd bucket of around 10% for emergency expenses, 4th bucket of 5 10% for savings and 5th bucket of remaining for family expenses inclusive of family holidays.