I am not answering your question but adding a question from my side? What other factors  related to nutrition 0-5 years will be collected inn the sample for all groups?

You actually pose multiple questions, none of which are formulated precisely enough or in sufficient detail to give a succinct answer. I will try to explain myself below.

First, I am not sure what you mean by "to determine the differences in…". You don't need to calculate sample size to determine differences; such calculation is only necessary if you want to determine with statistical significance if there is indeed a difference, or if you want to put confidence intervals around a point estimate of the difference. Regardless, you need to define what indicator or indicators you will use to measure body fat composition and any other outcomes of interest. Each indicator has a different level of random and/or systematic error which would then influence the dispersion of data values which has a direct effect on required minimum sample size. Once the indicator is defined, you need to make assumptions about how big a difference you expect to see and what will be the dispersion of the values for this indicator. In addition, will you compare measurements of body fat in the same children when acutely malnourished and then again when they have recovered from their malnutrition? If so, then the sample size calculations must account for the decreased variance because you have eliminated inter-individual variability. So, as you can see, calculating the minimum required sample size is impossible without more specific information.

Second, let us address determining associations between anthropometry and body composition indices among studied children. As above, calculating the sample size to answer this question requires identification of the indicators used to measure "anthropometry" and body composition. In addition, will such an association be explored using continuous variables, such as weight for height z-score and percent body fat? Or will such an association be explored using categorical variables, such as the presence of moderate wasting, severe wasting, and no wasting? The calculation of minimum sample size is entirely different for these two situations. In addition, the calculation requires an assumption about the dispersion of the indicator data; is this know for percent body fat in young children?

Finally, you asked about the determination of whether or not anthropometric and body composition indices are different between different groups such as age, sex, caste, and other demographic indices. To calculate sample size to answer this question, we have to know exactly what and how many subgroups will be compared. For example, will age be dichotomized into only two age groups, or will 10 age groups be formed each one of which is only six months wide? The calculation of minimum sample size is entirely different in these two cases. How many castes will be compared? What other demographic indices do you plan to compare and want to calculate sample size for?

Of course, sample size depends upon the study design, especially how study subjects are recruited. If the recruitment is clustered or stratified, this must be taken into account when calculating sample size. So you need to determine the methodology of your study before you can calculate sample sizes for your principle outcomes.

In general, for any given study, once I have determined the basic study design and recruitment methods, I try to identify a few primary outcomes for which to calculate sample size. For each of these, I define the specific indicator to be measured and investigate what assumptions should be used in this calculation. For some such questions, a pilot study may have to be done in order to formulate reasonable assumptions to calculate sample size. I suspect that this may be the case with your inquiry.

I would strongly recommend that you identify a competent epidemiologist/statistician with whom to work in person and in real time. The sample size calculations you request will take a great deal of further consideration, negotiation, and discussion among all the researchers involved in the study. This is not something that can be answered in a post on en-net.