Does this work in places other than Europe? Such as China, India, Ethiopia?
It works in 170 international countries. I've only traveled to Europe mostly, so I can't provide and feedback on the countries you mentioned. It does appear to work in some of the ones you mentioned. You can check here for google fi international coverage:
https://fi.google.com/about/rates/
For 1 person:
Fi is $10/gb until 6gb then its unlimited, so esstianlly $60 (plus $20 base fee for a total of $80) for unlimited and you only pay for the data you use. If you only use 3.5gb, then you pay $35 for data (plus the base $20), you use 10gb you pay $60 (plus the base $20). We usually do 1 data/voice sim and 1 data only sim in our phones and then use whatsapp to communicate. Fi changed to a multi-person plan right after we traveled last year so we might actually use 2 voice sims this time depending on the cost.
If you've never heard of whatsapp, look into it. Its great for keeping in contact/messaging/voice messaging and actually calling people overseas on data for free (on wifi, will use data if no wifi) with no need for voice. This is how we communicate with our friends in Italy. Whatsapp is very popular in Europe.
I do not know of any other international plan where $80 gets you unlimited data for 1 person, $135 for two people total for international. Local sims may be cheaper but a lot more hassle depending on the country. I haven't looked though, we have verizon service and don't plan on switching due to coverage in rural IA. My parents place is one of the few where USC doesn't work.
Edit - Disclaimer: Fi and Whatsapp have worked well for us but YMMV.