Form 8990 is used to calculate the amount of interest expense deduction allowable in the current year as it can be limited by the amount of income of a business. Form 8582 is used to determine the amount of passive losses allowable to be deducted in the current year. They are two unrelated deductions so you wouldn't use one form in place of another.
Schedule E is used on your personal return to report rental income and also income/loss as reported on K-1 schedules from partnerships, S corporations and Trusts.
Your excess business interest is the amount not deductible in the current year as per the limitation calculated on Form 8990 mentioned earlier.
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