I need a statistician - help with statistical design and sample size calculations - cluster analysis (URGENT - grant submission)

The submission is intended to fund a research project looking at a possible transdiagnostic neurobiological mechanism between 2 neuropsychiatric disorder. It envolves 3 different projects - 1. A population based study, where we look at 2 experimental tasks in a large sample of healthy controls, that we hypothesize correlate with different self-reported symptoms. 2. A neurophysiological study in 2 patient groups and a HC group - in which we will measure 4 different EEG evoked potentials - along with the measures of self-reported symptoms as in experiment 1. - in this section we are planning to apply unsupervised data analysis in order to group subjects according to their EEG correlates. As we expect to be an overlap in different diagnostic categories that would then correlate with overlapping symptoms. This would allow us to overcome the oversimplification of diagnostic categorization only based on diagnostic criteria in psychiatry. Will need help in statistical design as well as sample size calculations