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Some do, but it is not required. The Gridcoin blockchain rewards the workforce of each project for free at some base level. If the researchers want to attract even more compute power, they have the option to 'rain' GRC onto their workforce through the Gridcoin wallet.

So is it similar to how the Steem blockchain pays content creators and curators but Steem users can also directly tip the content creators in order to attract even more quality content?

That is a really, really good analogy! Never thought of it that way, but the parallel is perfect.

No, the people mining (those running BOINC) are rewarded. The researchers (those who run the BOINC projects) only have to pay for server costs, not the miners.

What kind of servers?
Data storage or data processing?

The servers that handout the Work Units (the work that the researchers want being done). Each BOINC client communicates with the project servers to get these work units. So they send the raw data and receive the processed data. The processed data is also verified by other BOINC users. So no data processing is required on the server side.

I'll link some resources for any other questions you may have:
https://boinc.berkeley.edu/
https://steemit.com/gridcoin/@sc-steemit/eli5-gridcoin-research-and-boinc-explained
https://en.wikipedia.org/wiki/BOINC_client%E2%80%93server_technology
https://en.wikipedia.org/wiki/Berkeley_Open_Infrastructure_for_Network_Computing
https://gridcoin.us

If something isn't on there don't be afraid to ask!
Hope this helps start your BOINC/Gridcoin journey!