Why do we give foreign aid?

[Franknburger]

Firstly- because it tends to have a far higher return on investment (economically, and in terms of satisfying people's basic needs) than other foreign policy instruments, such as military interventions, peace-keeping, "war on drugs" (burning down cocaine plantations in Bolivia). etc., It is probably also a lot cheaper in the end than building fences around the USA, border and sea patrols, and the like.

Secondly - because the USA tend to have army or navy camps in quite a number of beneficiary countries, or use them as supply routes (e.g. Central Asia). Especially in the case of the US, there is a pretty strong linkage between the size of foreign aid given to individual countries and US military presence ( interests there.

Thirdly -- because a lot of money is flowing back. Fees for American (or European) consultants, IT & software purchases, power generation / water supply / road construction equipment, etc.

Fourthly - because the USA have a historic responsibility vis-à-vis most (West) African countries, the economies of which have been devastated by centuries of slave capture & trade (the same applies to many European countries as former colonial powers).

Yeah - and then there is that romantic, idealistic stuff about a world free of hunger and poverty, with reasonable access to education and healthcare for everybody. And, in fact, the world has made quite some progress over the last thirty years in these respects, so the money spent, and the work of the foreign development community (of which I am part) has obviously not been completely useless.

[Franknburger]

Firstly- because it tends to have a far higher return on investment (economically, and in terms of satisfying people's basic needs) than other foreign policy instruments, such as military interventions

I don't disagree with your point as a whole. However, empirically, military spending is actually the most efficient way to stimulate short term economic growth through government spending: more so than welfare, healthcare, or public works (welfare and public works are both much better long term solutions, of course, and healthcare costs the government money, but life is a worthy cause, in my opinion). As a Democrat, it's not necessarily in my nature to want to uphold American militaristic spending, but it is flat out wrong to say that it is an inefficient use of money. Of course, this effect is on Americans and mostly only Americans. Foreigners are thrown under the bus by America, but then again, when are they not?

I take your point on military spending and job creation. However, domestic job creation is not among the traditional foreign policy objectives. Those are rather securing / promoting access to resources & markets, containing terrorism, controlling immigration, etc. If you do a cost-benefit analysis related to any of the a/m objectives, you will typically find foreign aid superior to the use of military force (which nevertheless may be required in specific situations).
Since you appear to have quite a good overview on available data and research: Is there any statistics available on the income US educational institutions generate from students from developing countries (including India and China),  and associated job creation in the US?
How much domestic spending on primary and secondary education has the US been saving by attracting immigration from developing countries? it was massive in the late 19th to mid 20th century, when most immigration was European, I wonder how the ratio is nowadays..