Index Construction and Factor Analysis after or before Multiple Imputation?

Background: So I have a dataset with 32 Variables. There are several missing values so I decided to impute them with the mice package in R. However, I plan to combine most of those variables through factor analysis, so that I am only left with 12 variables in my final analysis (with which I will conduct a multilevel analysis).

Question: should I combine the variables before imputation and then impute with my smaller 12 Variables or with the "raw" dataset of 32 variables?

I know you can do passive imputation, where you can include combined items, but I can hardly just use the factor scores from the unimputed dataset to be used in the passive imputation process like this (meth["Index1"] <- "~I(x1*0.789+x2*0.678+x3*0.786)", or can I?

Because here is another problem I have: I also read that you should include interaction terms, but my interaction terms will be between those indices. So I would need to have my indices already created in order to passively impute the interaction terms, or am I overthinking this?

I have read some similar questions here, but nothing that would really answer my specific question (1) (2) (3).