(a) Why are Singaporeans unable to retire in grace? Why has our CPF which is supposed to help us retire failed us?
This is a loaded question which makes presumptions that I'm not sure can be substantiated. Most Singaporeans are able to retire in grace, and the CPF has worked for most Singaporeans. There are exceptions of course, but that doesn't mean the whole thing is a failure. We will need to look at the exceptions in a case by case basis to see what the issue is, so if you know of such cases, perhaps you can elaborate on what happened.
These are the few cases I've seen so far that I can think of:
1. People with very little money in CPF because they are self-employed and never put money in their own CPF. They squander their cash and during retirement their CPF isn't enough to support them. The failure here I think is not with the CPF core, but the failure to set rules to compel self-employed people to contribute to their own CPF.
2. People that for some reason lose their house after retirement and have to pay rent with their monthly payouts. This is not really a problem with the CPF itself.
3. People that have to continue to work beyond retirement to support a more extravagant lifestyle than they can afford if they do not work. Not a problem with CPF which only specifies a minimum that you have to save. If you want to spend more during retirement then you need to save more when you are working. Sure, you can complain that cost of living in Singapore is high, but this is a cost of living issue not a CPF issue.
(b) Why are the monthly payouts subject to the whim of the govt which can decrease it anytime based on changes in mortality rates and inflation rates?
This is a standard thing used by all pension funds and financial institutes that sell annuity products, and it's not unique to the Singapore government. It's based on the basic financial concept known as the "Time value of money", there is a comprehensive article on wikipedia if you would like to know more about it. The same also applies if you manage your retirement funds by yourself.
Let's say at age 65, you have $100,000 and you somehow manage to find a bank that will give you 5% interest rate. You know that you will live exactly 20 years and will die at age 85. How much money then can you take out of the bank monthly so that when you die at 85, your balance is exactly $0? This can be worked out with a TVM calculator, e.g.
http://www.zenwealth.com/businessfinanceonline/TVM/TVMCalculator.html Set PV=$100000, Rate=5%, Periods=240, FV=$0, Monthly. Click on PMT to calculate the monthly payout, which will be $660. Now, see what happens if the interest rate changes to 6%, the payout increases to $716. If interest rate changes to 4%, then payout decrease to $606. If instead you expect to live 25 years until age 90, change Periods to 300, and the payout reduces to $585 for 5% interest rate.
(c) Does the govt serious expect a person to survive on a few hundred dollars of CPF Life payouts every month when the cost of living is so bloody high?
Assuming that your house is fully paid up, then yes, you can survive on a few hundred dollars per month in spite of the high cost of living, spending only on necessities. If you want to live a bit more extravagantly in your retirement, then you will need to save more money than the CPF compels you to with the Minimum Sum.
(d) Why is our CPF savings interest rate one of the lowest if not the lowest of all national-level retirement schemes in the world?
This is another loaded question. You will need to provide evidence of this. Also, note that you will need to take into account national interest rate as well as inflation rate when doing the comparison. Also, since you are comparing retirement schemes, you should be comparing against the CPF-RA rate of 4% + 1% bonus for first $60k