I am going to assume this is for SharePoint 2013.
Only one web application in your farm can support HNSCs in it.
This is false, but it is the recommended way to do it for manageability.
Use multiple web applications with host-named site collections
If you use more than one web application, you add more operational overhead and complexity to the system. We recommend that you use one web application for site collections.
Your farm can still support multiple web applications.
True, as per the above quote.
One web application can contain be HSNCs and path based site collections.
Do you mean contain both HNCs and path-based site collections? If so, yes.
Mix host-named site collections and path-based site collections in the same web application
You can use host-named and path based site collections in the same web application. To ensure that both types of site collections are accessible to users, do not put host header bindings on the IIS website of your web application, including IIS websites for zones that are extended from the web application. If an existing web application has a host header binding set, IIS will not return pages from the host-named site collection until you remove the binding from IIS.
See Host-named site collection architecture and deployment (SharePoint 2013)