Search API view doesn't display placed block
Database Search Default module expects the page and article content types that exist with the Standard Drupal install. You should be able to recreate these content types (and then later delete them) if you want to install that module. You should create Page|page, Article|article and keep both with the default body field. I think that'll be enough to let you install the Database Search Default module and see the configuration. You'll probably want to remove the configuration for page and article from the search configuration before you delete the content types.

If you don't choose to expose your form in block than you cannot place the form as a block on a page. If you're search results view is a block then I believe choosing to expose the form as a block will not work at all. If you want to expose the view as a block, you'll want to be sure that "Exposed form in block: No." Alternatively, if you're view is a page and you want your form to be a block, "Exposed form in block: Yes" and make sure Ajax is not enabled. (Afaik, Exposed form in block and ajax are not compatible at this time.