Yes to questions 1 and 3. There's also a "Japan Taxi" smartphone app you can use to call a cab to your location. Taxis are usually easy to find at hotels, stations and tourist sites, and may or may not be easy to find on the street depending on location and time.

Tokyo flag drop is 410 yen for the first 1.052 km. In Kyoto the flag drop is 590-610 yen depending on size but that covers you for 1.7 km.