That is exactly what Google custom search is for. Make a search engine while logged into your Google account and you are good to go.

but is that for searches on my website only, or a full search engine for the whole net?

Here are your options:

Your site only
Entire Web
Your site + Entire Web

Does this mean if I use the "search box" within my own site on my own computer then click on the link I have interest.

This is allow ?

Thanks

You can't click on any advertising link, no.

guess that mean I should not bother using the search engine within my own site right ?

I mean if you are planning to run a search engine and thinking of clicking your own ads you really have no business here. Remember that search engines are successful only when you have massive number of visitors because people come to click on search results not on ads.

The search ads seem to pay a lot less then content ads as well. I'd sneak in a content ad next to your results; I think you can put one content ad on the page according to the TOS.

I use the search box on my sites quite often (is it a good thing or a bad thing that its faster to use google to search my sites than it is to open my database? Hmmm...).
I *never* click on the google ads in the results.

(stoutfiles: I see higher ecpm for my search ads results quite often)

Me too, which actually surprised me. Last year when I tested Google Custom Search as a replacement for AdSense for Search, the revenue plummeted, but this year, now that they have replaced one with the other, it seems to be normal, if not better. I've seen search clicks above $2.00 in the past couple weeks.