If you want that all site collections will point to the Search Site, do you need to configure all Site Collections one by one? Is there any way (powershell or something) which you can use once to configure all site collection? thanks for your advice.
Here is what you are looking for. I have used this when I had to recreate my search center and it worked like a charm:
All you basically do is save your new search center url in a variable and use that variable to set the url to all sites within a web app by iterating through them.