It's a bit difficult to give an estimate with the information provided. I'm not sure if your question is related to adding privacy to an existing server code or you need the whole server side done. The later is significantly more cost and has an unknown scope based on only the info given. You ...
It's hard to get a definite answer to this as these companies will not tell us how their algorithms work. Having said that: Based on my experience working with these APIs, it is totally possible to implement a real-time search like "socialmention.com" purely based on the APIs from Google, Twitter...