Do I have a moral obligation to give money to charity?
Do we have a moral 'obligation' to do anything? I could argue for why you should give money to charity; I could probably argue for why you should not. At what point do you become bound to do something? Even if you make a promise, you can still choose not to (and what if, after making such a promise, it occurs to you that the keeping of the promise will bring about harm rather than good?).
I could argue that you should give money to charity because there might come a time when you will need it to be given to you. I could argue that your upbringing - at least in the UK - is largely as a result of public funding and that you have an obligation to give back to society for what it has provided for you. All of these things I could argue but I don't think that I could oblige you to be charitable unless you desire to do so.
On a national level, should the governments of countries which are heavily in debt still give overseas aid money?
We could take a Kantian perspective on this and argue that no, they should not; this is because they do not have the money to give and that if 'ought implies can' then they 'cannot' so it follows that they 'ought not'. However, perhaps if they have entered into a charitable relationship with another country then they must factor this into the money they accrue from borrowing.
Also, we can ask what would happen if they did not give aid money if they were in debt - given that many of the richer countries have only been able to keep themselves afloat (and often barely) with financial assistance it follows that they would cease to give such aid and many peoples dependent on such charity would die. This might be contradictory, insofar as the reason for the richer countries borrowing money is to keep the economy afloat for the well-being of their citizens - however, alongside this their unwillingness to give aid could result in a greater share of the total world population suffering even more greatly. This is, essentially, a display of double standards.
However, a government is always under scrutiny from the citizens it purports to govern and it is in their interests to remain in power (and maintain a more general confidence in political institutions) in order to enact policies which will, hopefully, lead to a better quality of life for these citizens; as such, it needs to show that it puts them before citizens from other nations.