I have a dataset of around 25 observations and most of them being categorical. I have three questions for this. 1- Do the covariates I pick for hierarchical clustering matter or should I try and include as many covariates as I can? 2- Is it possible to do hierarchical clustering for the whole data set, including the categorical data? 3- I want to reduce the levels on two covariates. My thought was to do hierarchical clustering for both of them using the same variables. I won't be using the results from one cluster in another. Would I run into any problems by doing this?
HAC can run on any distance matrix (although some variants such as Ward assume it is Euclidean or squared Euclidean, so check the documentation!).
In particular, you can try a Gower distance matrix.
The main problems with categorical attributes are: weighting because the features usually are not all equally important and interpretation of the results. Sure, you got clusters. But are they better than "random"? You can get almost any result just by playing around with the parameters.