Global modifications to sites can be achieved with an SPFx extension - application customiser. There's plenty of info about how to build one in the MS docs, but here is an example of what you are trying to do, I think:
SharePoint Server 2019 does not have hub sites nor will it. SharePoint Server 2019 is a 'snapshot in time' with certain features adjusted/removed from SharePoint Online -- SharePoint Online did not have hub sites at the time the snapshot was taken.
Nothing as far as I know. SP2013, 2016 and 2019 all have the same compatibility level (15, in this case). The only issue you’ll run into is if you’re accessing something in 2016 that doesn’t exist in 2019.
I’ve successfully deployed WSPs built for SP2013 (exact same file) on SP2019 and the functionality was running as expected.
You can create a .ts file with necessary information and import it anywhere in your web-part project.
Reference: AppSettings in your SPFx solutions
You can create a property pane field to pass the Result Source GUID and use it in your web-part.
Reference: Make your SharePoint client-side web part configurable