sure. If you know how to find the data in the html of the page, there's nothing preventing you from extracting that data (except maybe knowledge of the tools you elect to use to do it).
Any programming language that can handle blocks of text will do.
Depending on the details of how you plan to find the data you may be able to use more advanced tools like regular expressions to get you to your target more quickly, but there's certainly no requirement to use them.
browsers generally save whatever they download somewhere, at least temporarilly.
But that's irrelevant, as any program that needs to parse html and interpret the results will have to download that html itself.
It's easier that way, and you don't introduce dependencies on system specific settings (like installed browsers, where those browsers cache things, if they cache things at all, etc. etc.).