[susan53]

With regard to your second question - I'm not sure if you're asking about a) the word money in particular, b) about uncountable nouns, or c) about all nouns. However, if (a) or (b) - yes, it's fine without a quantifier. You can often check if something is said just by googling the phrase. If it comes up regularly on British/Australian/Canadian/American etc etc websites, you know it's used frequently.

Personally, I'd tend to use the quantifier if I wanted to know if someone actually had cash on them at that moment - eg if my son was going out I might say : Have you got some money? / Take some money with you or Do you need any money?

The same for other uncountable nouns - eg if I was cooking in someone else's kitchen, I think I'd say Have you got any/some rice? rather than just Have you got rice? But it's perfectly possible without the quantifier.

And in other contexts it sounds better without the quantifier :

Here are some examples I found on Google :

Have you got money owed to you?
If you're owed money...
Does someone owe you money...
Do you have money invested in the stock market?
Have you got money invested in that movie?

In all of these examples a quantifier would be possible - some, any, a lot of, a little etc. I'd suggest it's omitted because the speaker's focus is not on the quantity - it doesn't matter how much, whereas if I want to know about my son/the rice, the quantity is important - I need to know that he's got enough money to do what he wants, or there's enough rice to cook what I want. So the concept of quantity is implicit and leads to me choosing to use the quantifier.