Does the income cover the rent?

It is a long-standing industry convention that maps to spending roughly a third of gross income on housing — the same threshold at which housing researchers call a household cost-burdened. It persists because it is simple, explainable, and applied the same way to everyone. It is a convention rather than a law, and some markets commonly use 2.5×.

Gross — income before taxes and deductions. That is what employment letters and pay stubs state cleanly, so it is the basis screening standards use. If you switch to net income you would use a lower multiple; mixing the two (net income against a gross-income multiple) rejects people the standard would actually pass.

Not uniformly. Several states and cities regulate how income standards may be applied — for example, requiring that housing vouchers count toward income or limiting income multiples for voucher holders. Fair-housing law also requires applying whatever standard you choose identically to every applicant. Check the rules where the property sits before publishing a requirement.

Common practice is to combine roommate incomes toward the multiple, since the lease obligation is shared. Where an applicant falls short, many landlords accept a co-signer or guarantor, often held to a higher multiple of the rent because they are backstopping a household they do not live in. Whatever you allow, write it down and apply it consistently.