You can encrypt any file with any password. Of course, you need to do so manually. If you want to automate that process then you would need some custom solution.
1 – Plugins are written in C/C++.
2 – You need the plugin to communicate with Acrobat BUT it could be controlled by a separate program. (so the actual encryption would be controlled by the plugin, but the names, passwords, ,etc. could be driven from outside).
3 – The SDK documentation is it.