Hi.
1. The job search result page uses the layout of the job archive page. If you want to change the heading background image, please go to Customize/ Job & company/ Job list/ and change the image of the Job Heading Background image config.
2. Use the 3rd plugin as the Loco Translate plugin and find that string in our language file to change to another string as you want.
3. We have supported some fields for the heading search. Please check it at customize/ Job & company/ job list. https://prnt.sc/qqgxVfl4o5LO
Or you also can use the search sidebar widget of the job archive page.
Please recheck it.
Thanks.