Tor Project's Orbot/Orweb (free download) takes care of this problem.
Your info is encrypted and IP number is hidden. Some sites (including this one) may reject your attempt to log in, but this is the way to fly if anyone desires to be incognito.
No, no it does not. Tor is meant for anonymitiy, not privacy. Any of the Tor exit nodes can determine your searches or other material and it is not that difficult to de-anonymize a Tor user. In fact, a lot of .gov agencies run Tor exit nodes specifially for this reason.
It will make lacing together your activities more difficult, but absolutely not private. There are lots of ways to fingerprint a unique user based on their browser type, phone type, IMEI and other details sent with each search.
First, this GPS/location subject is so pedestrian that I completely missed the question's meaning! Very simple answer for that one. Turn your phone off. Turn it on only when you need to use it. Otherwise, the phone is in constant communication with the network carrier and your location always known. With or without GPS enabled. I leave my phone and GPS on. Who gives a care where I am? Use DuckDuckGo for a search engine. They don't track users. None of us are fooling anybody!
Anonymity trumps privacy. When you are private people know who and where you are but not what you are doing. Privacy still identifies you and still gives any meddler a starting point to begin looking.
Anonymity means that nobody even knows who you are, let alone where to start looking. Orbot is the best way to travel. Data is encrypted and sent https through out its journey. The only real weak leg is from the final tor exit mode to the final destination. There you can search for anonymous, encrypted data coming through with a different IP number than original. Good luck!
Orweb is a simple tor browser. It has only one tab, no bookmarks and saves no info. Orfox is a new, free, tor browser that operates just like its sister Firefox.
Another thing that tor can do is access the Deep Web. Those .onion addresses. Over 90% of the web does not exist without tor. Try Hackaday.onion on your iphone. Hows that working for ya? Now try Hackaday.io (a sister site accessible from the internet). Understand now? Didn't even know things like that existed, did you?
This is a very big world. We are all microscopic people in it. We all do well to listen with our ears instead of our mouths.