Is it true that Google tracks us?

Theres a rumor to that effect and I haven't been able to verify this as true or not  but anything is possible nowadays and Google has been know to work with the Federal Government but we will know one day

Pretty much. That's not necessarily a bad thing. It means that when you do a search you are likely to be given better results based on your location and preferences.

They use the information gained to present you with the most tempting ads. That's not too much of a problem if you use something like "Adblock Plus" which will remove ads from your monitor.

Yes. Just your usage data to fine tune user experience. Android (Apple too) phones track your rate of movement so they can give precise travel estimations when you look on your digital maps and tell you which intersection is having a bad time. However you should be more terrified of 3rd party apps that you get on Facebook or download to your phones.

I heard a rumour that Google tracks our phones and they determine the amount of traffic on the road by the speed that the phone is moving

Yes, but they use the information for ad targeting and better search results, you can avoid being tracked by using adblock and disabling 3rd party cookies in your browser.

PS. Your internet provider also keeps your browsing info. Everything you do on the internet is not a secrete. (if the government wants your info, they will give your IP a warrant for it).

Yes, and their privacy policy and terms of use is buried in so much legal jargon and red tape, it's impossible to figure out what exactly they are tracking and what they use it for. We do know that google search histories have historically been subpoenaed for court and used in criminal proceedings. 

That really opens up to the fact that they can be used for anything really, whether or not Google themselves is misusing the info, I don't think many really know.