You can always run the ANOVA, regardless of how many data points you have. Just don't expect significant results if there are too many degrees of freedom and not enough data points.
In R, you can fit a regression model with categorical variables and then call anova() on your model.
Based on your causal diagram, it appears that "selection variables" refers to confounders, not factors related to selection into the sample. This distinction is important because the items included in the different inverse probability weights is important.
Briefly, to answer your question, I would not use any of the approaches you listed. The analysis and ...