Q. Can I add my brother, who's on an F1 visa, as a dependent in my tax returns?
A. No. A person on an F1 must be in the U.S. for 5 years, to be considered a resident. Being a US citizen or resident is a requirement (residents of Canada and Mexico are exceptions). You probably also don't meet the support test (rule). See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
Q. If me and my brother live in different locations, will that be an issue?
A. No. There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" [QR] in IRS parlance even though they don't have to actually be related). There is a residence test, for a QC, but not for a QR.
Q. How much max tax advantage can I get if I add him as a dependent?
A. A Qualifying Relative dependent is worth a $500 "Other dependent" non-refundable tax credit.
Q. What are the proofs needed to be submitted along my tax returns to add him as my dependent?
A. None. Proof is only necessary if you are "audited".