Let's Encrypt can issue ECDSA (P-256 or P-384) certificates, but the current intermediates and roots are RSA. ECDSA intermediates and roots are on the to-do list.
3072 is allowed. I think the maximum is 4096? 2048-bit RSA is not likely to get broken any time soon, though.
Yes. Well, technically, there's an option to specify the CSR to use. However, Certbot current'y doesn't support automatic renewal with custom CSRs, so the usability is worse, and you may be happier with a different client.
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