Most of highly used APIs (google, facebook..) have short-time limits and long-time limits for better control over traffic. It allows developers make many requests (eg. 20000 per day) but prevents throttling if someone would try to eg. send 1000 requests in one second, which could clog api endpoint.

What you have in your google console:

Project per-second limit per 100 seconds = 1

That means you can make 1 query for 100 seconds in each project.

And:

User per-second limit per 100 seconds per user = 1

That means you can make 1 query for 100 seconds for each user connected to project.

That two limit rules putted together dont make much sense beacuse second rule will never be triggered (both have 1 request per 100 seconds but first one is for 'higher' resource and will block more requests).

Example of many limits you can see eg. in Analytics API where we have:

Queries per day = 50000

Big limit for queries per day.

Queries per 100 seconds per user = 100

Small limit per 100 seconds and per user so they can prevent too high peaks of requests from single user.

Queries per 100 seconds = 2000

Medium limit per 100 seconds.

This is for a custom search, not a normal Google search. For example, if you owned abc.com and acme.com, you could set up a custom search on those two domains for your customers. That way, they could search your sites for information. The 5,000-site limit is actually huge. I'm not sure I can think of an application that would use that many specified sites.

I think what you are looking for is the Google Web Search API, which searched all of Google. Unfortunately, that is now depreciated. (reference: http://code.google.com/apis/websearch/) You can still use the old API, but it is a risk because Google reserves the rights to turn it off at any time. They will also limit the number of searches you perform per day (although I can't find a specific number for that limit). Here is a link to their terms: http://code.google.com/apis/websearch/terms.html

I would recommend looking at an API from another search engine if you really want to integrate it directly into your code. A different suggestion would be to put your search information behind an interface and code it to Google for now. Then if they turn it off or something better comes out, you could change just the search code to point to the newest and best API.