What is the ratio of EAs in major altruistic movements such as global poverty, animal rights, and environmentalism?
All three of those movements have enough supporters that EA is no more than a tiny blip. However, farm animal welfare in particular has been dramatically influenced by a large amount of EA funding into a sub-area of animal welfare that had been relatively obscure. I can't find the reference at the moment, but a 2019 EA Global speaker estimated that the fraction of farm animal welfare funding from EA sources was (if I recall correctly) somewhere between 25% and 50%.
EA-type methodology (though we certainly didn't invent it) has become much more popular among academics and policymakers focused on global poverty (the most recent economics Nobel went to three academics who popularized it). I would guess, from my experiences working with academics in this field, that most such academics are aware that "effective altruism" is a thing, and perhaps even that GiveWell exists. I don't know what fraction would self-identify as "EA", however.
How "big" EA is in governments?
Rachel Glennerster, the head of the UK's foreign aid department, is an avowed member of the EA movement. Martin Rees, a major longtermist scholar, has been knighted by the British government. A few British MPs are also quite EA-sympathetic.
J-PAL and IPA have placed a lot of advisors (perhaps dozens?) in various developing-country governments over the last few years, being helped in many cases by people inside those governments who were interested in using a quantitative/experimental approach. However, I again don't know what fraction of these people would self-identify as "EA".
I'm not aware of any major politicians outside the UK who have made public endorsements of EA or any of EA's more unusual causes (unless you stretch to include Andrew Yang). But I could easily be unaware of one or more such people!