I would expect the number of ea-but-dont-know-about-ea people to be pretty high actually. Givewell received $42 million last year from people who gave $1 million or less, if each person gave $5000 (which I think is a generous amount), that's 8400 donors compared to the 3,500 that took the EA survey last year. Of course that could just be cause most people don't like taking surveys, but I would expect that to be countered by a lower average donation amount. In contrast, taking the median estimate of $750 in the last survey, it looks like we have 56,000 self-reported EAs (or at least Givewell EAs), that seems kinds high to me.

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!

Answer from Rethink Priorities (2020): estimate there are around 2315 highly engaged EAs and 6500 (90% CI: 4700-10,000) active EAs in the community overall.

There are 17,571 people in the Effective Altruism Facebook group, as of today (November 23rd, 2019).