Google is embedded in most web services, including this site (as capcha via cloudflare). But, you eventually would learn that non-google services that are mostly as good (except maps), and you would use no-script.
Not really no. Security wise, they remain one of the most badass actors on the field. I am very sure that my data and passwords are safeguarded. Same can't be said about Yahoo, Bing, or other companies/products.
Like, lawyers have their own collections of research they search through, and because they're not all SV tech bros, they're not above making a phone call or meeting in person in one of their offices (and no, not the open kind).
There exist other quality search engines like DuckDuckGo. As for anonymity of location: Google would most likely have someone dig through search queries done in the city of the plaintiff/lawyer. VPNs and proxies can help as well as services like Amazon Workspaces. Combining both will mask any trace of your identity pretty well from all but the big 3 government agencies.
How do you do research? How do you communicate with your lawyer?
They know everything about what you do, when you do it, and who you do it with.