Display Product Code/ID

Yes. Turn on the "show product code" option in the Display tab of the configuration.

It means that you're not using the latest version of HikaShop.
You would have to update.

The error
Fatal error: Maximum execution time of 30 seconds exceeded in /home/fhlinux142/d/draganfly.co.uk/user/htdocs/libraries/joomla/filesystem/archive/zip.php on line 351
means that because of the restrictions on your webserver, Joomla didn't had enough time to extract the archive of HikaShop in order to install it. HikaShop is a big package.
Please follow the install via FTP and that will avoid the problem:
www.hikashop.com/en/support/documentatio...-to-install.html#ftp

In the hikashop search plugin options, you can select the columns on which you want the search.
There is no option to display the product code in the search results.
You would have to edit the file plugins/search/hikashop_products/hikashop_products.php and change the line:
$select = ' a.product_id AS id, a.product_name, a.product_created AS created , a.product_description, "'.$new_page.'" AS browsernav';

to something like that:
$select = ' a.product_id AS id, a.product_code AS product_name, a.product_created AS created , a.product_description, "'.$new_page.'" AS browsernav';

so that it displays the code instead of the name.

Unfortunately, the joomla search is quite limited in display options :/
With the modification I gave you in the plugin, we're already reaching the limits.

That would require to modify the display view of the search component of joomla.

You could try that module yes. There is a plugin for the integration between that module and HikaShop that you can get here:
offlajn.com/blog/entry/2012/02/10/improv...r-joomla-151725.html

Otherwise, it would require to use a HikaShop filter module since the results of the filters of HikaShop are displayed as a normal products listing:
www.hikashop.com/en/support/documentatio...-filter-listing.html