In the STATA survey set, you need to declare the PSU (DHS variable V001 or V021), but not necessary to declare the SSU (DHS variable V002), if your aim is to produce sampling errors. You do not need to declare the fpc because it is not provided in the DHS data.

As has been noted in other posts, we are unable to separate out the probabilities of selection for the cluster (v001 or v021)) and the household (v002). What we have is the product (the second probability is conditional on the selection of a cluster). There is no way to separate the two. That's unfortunate, and it means that svyset cannot be properly constructed for multi-level models. The basic reason for this is that if the separate probabilities were available, then the first one, with a little additional information, would allow one to identify the PSU. DHS does everything possible to protect the privacy and confidentiality of the respondents. Apart from that, the required information is deleted after the weights have been constructed. We couldn't retrieve it even if we wanted to.

There is definitely some clustering of child-level outcomes by the mother and/or household. At DHS we do not adjust for that, but you certainly may want to do so. A complication is that the number of children per woman is low, especially if you are focusing on outcomes within a recent time period and on children in a narrow age range such as 0-4. Other users may be able to suggest how to specify svyset for such outcomes.