If you mean customize the code then you can modify mod/database/tabs.php to comment out the line that adds the search tab, and mod/database/lib.php function data_extend_navigation to comment out the line that adds the corresponding link to the navigation block.
Other possible approaches, less foolproof though, are css and/or javascript to remove/hide the dom elements of the tab and navigation link.
hth
According to the view screenshots you uploaded a zip file which presumably contains a pdf file. In order to display the the pdf icon and the file name you need to upload a pdf file. Now, the field pattern will display the file name as a link to download. If you want the link to read 'Download file' you need to change the file name accordingly. Alternately, you can add the text Download file above the file link. The only problem with the latter is that the label will be there even if no file has been uploaded to the entry. hth
Can you post screenshots of the fields list and the view template?
Not entirely clear on what the requirement is. Do you want to show the names of files uploaded to a Database activity?
Afaik there are no plans to replace. Functionality is added to core Database module based on community interest and contributions as with other modules and components.