It sounds like your contact form isnt working and therefore I would contact your designer and demand he fix it as you are paying him £150 for maintenance.

As for links, I suspect he may be on about backlinks eg links on other sites pointing to yours. These are important if you want to rank highly in search engines. Again check your contract and see what it says about search engine optimisation.

Can you post a link to your site so we can check how it is doing in search engines.