The IRS considers an incarcerated spouse to be temporarily away from home. That does not have an effect on your marital status or your filing status.
The choice to file using either Married Filing Jointly or Married Filing Separately filing status is yours. In most cases it is better for a married couple to choose Married Filing Jointly filing status, even if one spouse had little or no income. This allows you the possibility of claiming several tax credits that are disallowed to Married Filing Separately filers. In addition, you benefit from the higher $12,600 Standard Deduction and both (your and your wife's) $4,050 Personal Exemptions.
Amounts received for work performed while an inmate in a penal institution aren't earned income when figuring the Earned Income Credit. This includes amounts for work performed while in a work release program or while in a halfway house.