Is the website accessible? IF yes then i can easily do the corrections without resorting to manual correction. Well Even if its not accessible I can still do the same haha. With over a decade of experience as a full-stack developer and IT professional, I have a deep understanding of WordPress and its intricate workings. This includes working with large, high-traffic websites and dealing with complex issues such as yours. My skill-set, specially honed in HTML, MySQL, PHP and WordPress, absolutely aligns with what you're seeking for this project.
To deal with the issue at hand - fixing broken images, non-functional download links and updating URLs at scale - I can leverage my expertise to automate the process. Instead of going through each post manually, which as you've mentioned is impractical and time-consuming given the enormity of your site, I'll write custom scripts for bulk modifications.
Your website's database issue - 'siteurl' and 'home' fields missing from wp_options table - can be resolved without any hassle. With proficiency in MySQL database management, I can quickly rectify this issue for you.
In short, my combination of technical know-how, problem-solving skills and propensity for close attention to detail makes me an ideal candidate for your project. I assure you the job will be delivered to perfection whilst respecting your budgetary concerns. Let's get started on revamping your site today!