Links not working on migrated site
I feel you're missing .htaccess file. Usually its a hidden file, so make sure to show all files (including hidden files) and copy it and paste it into your local drupal folder.

Also, make sure you local server has mod_rewrite enabled to support clean URLs, if its not enabled then check this answer: How to enable mod_rewrite in Apache?.

Another suggestion is; to turn off Clean URL from settings.php by adding the following code:

$conf['clean_url'] = 0;