Glad to see you're interested in the topic of moral circles and how they influence people's behaviours!

1.

What research exists for "moral circles" in general? It seems that MichaelA mostly referenced other forum posts more than scientific literature.

My post indeed primarily referenced non-peer-reviewed sources (with the main exception being Crimston et al.). But I've collected some relevant peer-reviewed sources here (go to "Academic works") and here, which you might be interested in checking out. As I say in the former collection:

There appears to be a substantial and continuing amount of psychological work on this topic; the papers I list here are just a fairly random subset to get you started.

I'd also add that many of those papers are quite recent (rather than e.g. them all being from decades ago), so I'd guess that we'll continue to see more work on these topics in the coming years.

(By the way, the key reasons I mostly read and cited non-peer-reviewed works were that (a) I thought that they might be more relevant from an EA perspective, and (b) work on moral circles was kind-of a tangent from my main research focuses, so I didn't want to take the time necessary to properly immerse myself in the academic work on it.)

2.

Is it just too difficult to measure/categorize an individual's actual moral circle?

Crimston et al. is a good source on this sort of question, and I think it indicates the answer is probably "no". Here's the abstract:

The nature of our moral judgments-and the extent to which we treat others with care-depend in part on the distinctions we make between entities deemed worthy or unworthy of moral consideration-our moral boundaries. Philosophers, historians, and social scientists have noted that people's moral boundaries have expanded over the last few centuries, but the notion of moral expansiveness has received limited empirical attention in psychology. This research explores variations in the size of individuals' moral boundaries using the psychological construct of moral expansiveness and introduces the Moral Expansiveness Scale (MES), designed to capture this variation. Across 6 studies, we established the reliability, convergent validity, and predictive validity of the MES. Moral expansiveness was related (but not reducible) to existing moral constructs (moral foundations, moral identity, "moral" universalism values), predictors of moral standing (moral patiency and warmth), and other constructs associated with concern for others (empathy, identification with humanity, connectedness to nature, and social responsibility). Importantly, the MES uniquely predicted willingness to engage in prosocial intentions and behaviors at personal cost independently of these established constructs. Specifically, the MES uniquely predicted willingness to prioritize humanitarian and environmental concerns over personal and national self-interest, willingness to sacrifice one's life to save others (ranging from human out-groups to animals and plants), and volunteering behavior. Results demonstrate that moral expansiveness is a distinct and important factor in understanding moral judgments and their consequences.

3.

I have some intuitive sense that as your moral circle expands or intensifies for agents outside of yourself, your frugality increases, i.e. you spend less on yourself. Is there any research on this idea?

Unfortunately, I don't know whether this is true, or whether there's research on this specifically. My quick guess is that that's plausible, but not guaranteed.

One reason frugality might increase:

• You come to believe there is more suffering and more unmet potential for welfare than you previously did, which makes you see donating as more important or more cost-effective, which makes you want to spend less so you can donate more.

Some reasons frugality might not increase:

• You come to believe some additional entities deserve moral concern, but this doesn't change your believe about what the most cost-effective thing to donate to is or how cost-effective it is (e.g., because anything targeting those other entities seems less cost-effective anyway).
• You come to believe some additional entities deserve moral concern, but you don't fully internalise that or act on it. (But I imagine some might say that this means those entities aren't "fully" in your moral circle.)
• You focus on increasing how much you earn rather than reducing how much you spend (with this still resulting in more donations).
• You think your main path to impact isn't through donations anyway, but rather through "direct work".

I think I'd personally be more interested in research on how differences in what entities are included in one's moral circle (and how much moral concern they're afforded) is related to or affects behaviours like donation amounts, donation targets, career paths, and voting behaviours, rather than frugality. Frugality seems interesting primarily due to how it might affect donation amounts, more frugality is neither necessary nor sufficient for more donations, and more donations is neither necessary nor sufficient for more benefits to the world.

That said, I do think frugality matters somewhat, and I personally try to be quite frugal, and this began partly due to caring about people in the developing world.

(Btw, I'm low on sleep today, so I hope that was all coherent!)