Is it possible to resize an image automatically, by letting Photoshop take the variable sizes from an external data (such as an Excel spreadsheet, Width and Height columns) and execute them and save them in a folder?
Absolutely. You can create a script (.js) to do the job.
If you're new to scripting Photoshop, check out some of the examples that come with it: they show opening files and doing operations.
NB. You might not be able to open your data file directly, in which case pasting it in (as csv, or json) into a
prompt call would possibly suffice.