Can I file as Head of Household if my adult brother lives in my house since I have always paid bills?

If he is a retiree and receives any type of income of $4,300 (Social Security benefits are not included) or more then you cannot claim him as a dependent.  Without a dependent on your tax return you cannot have Head of Household filing status.

Am I Head of Household?
https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household
https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household

That depends on several things.  The fact that he lives in your house is not enough.   Did he have less than $4300 of income in 2021 not counting Social Security?   Did you pay over half of his support?    If he cannot be claimed as your qualifying dependent then you cannot file as Head of Household.  

Am I Head of Household?

https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household

https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household

Yes, if he lived with you more than half of the year, you provided more than half of his support and he had less than $4,300 in taxable income.