Then every search you've ever made on Google when signed in has been associated with your IP address. Your internet provider knows who you are (your name address and probably a credit card #) and they certainly know what your IP address is and can be forced to give it up under certain circumstances. So, if certain authorities get the right warrants to present to both your ISP and Google then they can have all of your search data on Google, even 50 years from now.
If you weren't signed in then it wouldn't be there and couldn't be discovered, even with a warrant.
The difference between your ISP and Google is that your ISP isn't keeping a "forever" record of you search queries.
No.
1. My IP address changes periodically. I can change it at will, too. I think it's like this for almost everyone.
2. Your ISP knows where you live and every URL you've ever visited, and they always will even if you switch your IP address every second.
3. Even if you're not signed into Google, your ISP knows exactly what URLs you are going to. The feds can get a warrant...
4. You aren't forced to sign into Google. You're forced to get DHCP leases and request data from your ISP.
5. I'm not a terrorist or drug dealer, so no warrants are going to go out for me.