Can anyone see my Tumblr search history, like my internet provider or the legal & authorized government individuals?

I'll answer your question of Can anyone see my Tumblr search history from both options available -

Without a VPN Assuming that you are only using HTTPS, there will likely be a difference between your ISP and the government. This also depends on where in the world you are. In many countries your ISP couldn't care less about what you do. In some countries though, governments make the ISP care - sadly, the UK is now one of those places. An ISP will only have access to a log of the URL's you access so whether an ISP could track what you are following will depend on how you interact with Tumblr to follow someone. A government, on the other hand, will probably find a way to do whatever they want if they consider it important enough. So given that Tumblr is a public service and so subject to public scrutiny for its content and unless you live in a country with highly restrictive laws or you might be subject to professional blackmail (e.g. you are a teacher but show a liking for unpleasant subjects) and have a history of being in vocal opposition to your government, the risks would seem to be very low that anyone would really care.

With a VPN Your ISP can no longer track you at all. Once again though, a determined government attacker is likely to be able to eventually track you. The easiest way to do that would probably be to bug your house. Again, the risk is generally so small as to be insignificant unless you fall into the categories outlined above.