Can Google imprison you? Not in the US, unless their lawyers find a nice way to make a prosecutor go e.g. for some fancy computer espionage charges (see Aaron Schwartz for example), but companies in the past had regimes in their bag and made people go to prison or vanish entirely, or perform forced labor for them.

Can they seize your assets? Not directly, but try getting sued by the legal department of a mega corp and see what you have left when it's all over. The end result is the same.

As somebody else pointed out, we already had companies that effectively acted as unelected governments in the past, like the East India Company. They used to execute people.

Google can do bad things to you. Significantly less-bad things to you than imprisonment/asset seizure/execution, BUT they are not required to follow due process and are not answerable to anyone but themselves if they do something bad to you. They can also provide substantial amounts of incriminating evidence to the government (the ones who can execute you) and technically a warrant is not required. If the cops go to Google and ask for info about you that is stored on Google's computers, and Google gives it to them without a warrant, your rights as a US citizen have not been violated.

No, but they can effectively stop you from speaking online, which is what we're discussing.

They have your search history. Or they could make it if inclined. So for a lot of people, yes. They could easily put people in Jail.

More likely scenario would be exposing anyone That wants to be anonymous. Actually I think that happens in other countries all the time.

No, but they can use their enormous power and influence to get politicians into office that could write new rules allowing such.