If you access your personal email from your work PC (like you fire up your browser and go to mail.yahoo.com and start emailing away), then it is technically possible for your employer to see the contents if they have the right tools in place to do so. At my employer, we could monitor employees when they go to their personal webmail services, but we don’t. We just block those services.
It depends on lots of things. When you did the search, were you at home, at your employer, at the library? Were you logged in to your Google account while you did the search? The search provider and ISP(s) that carry the traffic will retain logs for some period of time. Depending on where you were connected at the time, the providers’ logs might point to an IP address that might be hard to link to you, or relatively easy to link to you. I don’t mean to be evasive. There are just a lot of variables, so it’s hard to give a short answer.
Then there’s the question of the browser history on your PC. How far back does your local history go, did you clear it, if so can any remnants be recovered?
Say you’re sitting at home, on a PC you own personally, getting internet service from your ISP. You Google “how to make strychnine”. Traces of the search will wind up in your browser history and cache. Google uses encryption now, so your ISP can’t see your search terms, but of course Google can. So Google sends you a bunch of results, including www . HowToKillWithStrychnine . com. You click that link. Your PC sends a request to a DNS server, which is probably run by your ISP. Your PC gets the DNS result and you get to the webpage. The webpage drops temporary files into your browser cache.
So, potential sources of evidence are your PC, Google’s logs, the logs on the DNS server, and the server logs at www . HowToKillWithStrychnine . com. It’s anyone’s guess how long those logs retained. Google might hold on to logs for 10 years (I really have no idea), but the other entities probably don’t. Logs take up a lot of space, and if they’re not relevant to your business you don’t keep them around.
Anyway, when your coworker keels over, the cops aren’t going to have easy access to any of this information. They’d have to go to multiple private companies and request logs in the hopes of finding something relevant. Or they’d have to get authorization to seize your PC and examine it. I’m not a cop, but I would think they’d need other reasons to suspect you before going to the trouble and expense of trying to resurrect your searching history from years prior. When your coworker dies, I don’t think the cops are going to immediately think, “Let’s get the search history of everyone the victim knew, going back 10 years.” It’s just really impractical, since you’d have to request information from lots of different service providers. It would also be a shitload of data that some poor bastard would have to sift through. And, I imagine the court might balk at a request like that. More likely, they’d have some other reason to suspect you, and as they were digging into your activity, they’d eventually seize your PC and go from there.