1. A website that might be running on a standalone server (which off late no body does) could be moved to cloud ( say AWS or Azure or Google cloud) by spinning the new instance of the web server (like apache or nginx etc.) and also migrating the relevant data and data store. We could do it like hot migration without bringing down the current website and once migration is done pointing it correct DNS entries to direct the traffic into cloud. Some cloud providers might be able to do it for you
2. I dont think anything needs to be done for "porting" it to cloud. unless the webserver's code is specific to particular operating system that cloud operator does not support.
3. Parallelizing and HPC could mean different. It depends what you want to run "parallelly" and what you mean by HPC ?
High Performance Computing most generally refers to the practice of aggregating computing power in a way that delivers much higher performance than one could get out of a typical desktop computer or workstation in order to solve large problems in science, engineering, or business.