Also, how can the government track our transactions?
That's what KYCs are for. Ever wonder why exchanges are asking for your KYC? It's really because for the government to track you and all the things that go in that exchange. Some governments even go as far as requiring the exchange to alert them when an unusual amount of money is going in and out of the exchange, they are also requiring them to send some random transactions from random users to see on how they earn (lose) money. Aside from that you are also in charge of documenting every gain/loss you have from every trade so that you yourself know how much you will pay depending on what tax rate you are in.