(I've split this question out from the previous thread just to help other users to find it more easily.)
I'll divide my answer up into sections to make this easier to follow!
1. Algún dinero vs. Algo de dinero
You’re right to say that algún is an adjective. It comes before nouns when you’re talking about something and you aren’t being specific. So, for example, if you say algún día, you’re talking about a non-specific day (i.e. “someday”), and if you say algunas personas, then you’re talking about non-specific people (i.e. “some people”).
This means that if you say algún dinero, then you’re talking about non-specific money. And it is possible to say this; for example, you could say something like No sé si tiene algún dinero en su cuenta “(I) don’t know if (he) has any money in his account.” However, often when you say “some / any money,” you’re referring to a non-specific amount of money, and that’s what algo de indicates. It essentially means “a bit of / any of.” For example, Necesitamos algo de dinero “We need some money” is more literally like saying “We need a bit of money” (i.e. “We need a (non-specified amount) of money”).
So a good rule of thumb is to use algo de with a noun when you’re talking about a non-specific, uncountable amount (e.g. algo de tiempo “some time / a bit of time,” algo de comida “some food / a bit of food,” algo de ropa “some clothing / a bit of clothing,” etc.).
2. Algo de + [Infinitive]
As for algo de before an infinitive, you can use it to mean “something to” in phrases like algo de comer “something to eat” and algo de beber “something to drink.” Once again, it’s representing an undefined amount of something.
3. Ningún and ninguna
These adjectives have a few possible translations, including “none,” “not any,” “not a single,” and, indeed, “no” – as in No tengo ningún tiempo “(I) have no time / (I) don’t have any time.” Since they are adjectives, you do indeed put them before nouns, and you can say things like No vemos ningún perro “(We) don’t see any dogs / (We) don’t see a single dog.”
For more information on alguno and ninguno, you may find it helpful to check out Lesson #11.8.
I hope that this answers your questions!
Hasta la próxima,
P.S. - I nearly forgot to mention: I'm not sure what you're referring to when you say that “it keeps throwing up algo de dinero” for “some money,” but do keep in mind that translation engines and the like aren't entirely reliable, and they will often only show you the most common translation they've found - not every translation that is possible, and not necessarily the translation that will work for your context. So it's best to avoid relying on them as much as you can!
I hope that that helps! :)