Živa Vidic, you can easily estimate a CFA model including binary indicators using a free R package called lavaan to find at https://lavaan.ugent.be/start.html. As far as I remember, I do not think that AMOS has any estimators for categorical data.

You seem to intend to employ a factor analysis of not only binary items but of a set of items including some binary items and some that might be treated as being ordinal (3-point and 5-point Likert scale items). I would recommend to first create a matrix of polychoric correlation coefficients (that can also be used for exploratory factor analysis) and use this correlation matrix as input for your factor analysis -- this is possible with various statistical software such as R, Stata, or SPSS. Note that tetrachoric correlation (for artificially dichotomous items) is a special case of polychoric correlation (for ordinal scale items) that will be identical to tetrachoric correlations of binary items. Thus a polychoric correlation matrix is quasi a natural thing to use if you have a mix of binary and ordinal scale items.

I agree with Dirk Enzmann to begin with a polychoric correlation marix. I also think you could look at using Mplus to use varying estimators that cope with predictors of different types (i.e., USLMV, WLSMV, and MLR, etc.)