Does it need to add redirect code to all pages on the clients website or does WP plugin does it automatically?

It's best to use the redirect plugin on your client's site. Install the plugin to the clients site and it will redirect to wherever you want.  Test it out by installing the plugin on your site and then all will be clear. 

If in worst case you mess something up you can always deactivate the plugin.  All you needs to do is install the plugin.

Script is only necessary for sites that are html only, which you are very unlikely to encounter.

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