In either of the first two scenarios where you charge rent, the rent is taxable income, but you can offset it with the portion of expenses related to the space being rented, up to the amount of rent received. So a portion of utilities, mortgage interest, repair/improvements, insurance, HOA, and you can deduct depreciation expense for the rented portion of your house.
Since you're married, you would only owe gift tax if you charged your sibling more than $28,000 less than market rate for the room in a given year. Reasonable market rate for a single room in a family's house is probably not $2,333 in your area, so gift tax likely won't be an issue.
To claim your sibling as a dependent they must either be a Qualifying Child or a Qualifying Relative. You'll have to look at the detailed Rules for Claiming an Exemption for a Dependent to be certain, but here's an overview of the rules:
Tests to be a Qualifying Child:
- The child must be your son, daughter, stepchild, foster child, brother, sister, half brother, half sister, stepbrother, stepsister, or a descendant of any of them.
The child must be (a) under age 19 at the end of the year and younger than you (or your spouse, if filing jointly), (b) under age 24 at the end of the year, a student, and younger than you (or your spouse, if filing jointly), or (c) any age if permanently and totally disabled.
The child must have lived with you for more than half of the year.
- The child must not have provided more than half of his or her own support for the year.
- The child must not be filing a joint return for the year (unless that return is filed only to get a refund of income tax withheld or estimated tax paid).
Tests to be a Qualifying Relative:
- The person can’t be your qualifying child or the qualifying child of any other taxpayer.
The person either (a) must be related to you in one of the ways listed under Relatives who don’t have to live with you , or (b) must
live with you all year as a member of your household (and your
relationship must not violate local law).
The person's gross income for the year must be less than $4,050.
- You must provide more than half of the person's total support for the year.
Given all that, I think it's likely just a matter of you picking a rent that everyone is comfortable with, and familiarizing yourself with calculating deductions associated with your rental activity, this nolo.com article has good info: Tax Issues When Renting Out a Room in Your House