Mixed types of data for clustering
You don't need to convert the attributes to numeric data for DBSCAN nor for HAC (hierarchical clustering).

What you need is a distance function.

While there are some such as Gower's, these are just heuristics.

If you want really good results, you need to carefully design a proper distance function that is able to quantify how similar records are for your purpose. This is very much usage dependent, and hence you cannot find the answer already solved for you.