“My fiance of 9 years was able to claim (take exemptions for) myself and two daughters from a prior marriage on his taxes since he met the IRS's Qualifying Relative rule, “==============>You and your two daughters from a prior marriage can never qualify as qualifying relatives on his return. He may claim you and your two daughters from a prior marriage as dependents on his return as qualifying non-relatives, NOT as qualifying relatives. You and your daughter are NOT relatives of your fiancé. You and your daughters, to be claimed as qualifying non-relatives, must have lived with him entire year. You cannot file a joint return using the Married Filing Jointly filing status unless you are legally married.
“and I had no income to file taxes their biological father was incarcerated with no income, making us both ineligible to file. Since he is a Qualifying Relative under the following rules:1. Not a qualifying child test, (passed);2. Member of household or relationship test, (passed);3. Gross income test, and (passed);4. Support test. (passed)”========> As said, your fiancé can never claim you and your daughters as his qualifying relatives NOT as qualifying non-relatives on his return.
“does that mean they are also his qualifying children so he can claim them for the Earned Income Credit and the Child Tax Credit?”=========>No; they are NOT his qualifying relatives but may be qualifying non-relatives . To claim the children for purposes of the Child Tax Credit, they must either be his stepchildren or foster children; For EIC , please follow the instructions here; Tips and Guidance for Determining Eligibility