With the travel time of 2 hours and 30 minutes, Nozomi Tokyo to Osaka one-way ticket costs around 160 USD. But keep in mind that such factors as preferred travel class or how much in advance you buy your ticket can influence the price quite significantly.
In many cases, flying is cheaper than riding there by bullet train. The easiest way to save on shinkansen costs is with an EX-IC card. You pay a deposit to get issued the card. Then, you download the EX App to your phone.
Trains rarely sell out except at peak travel times. The Nozomi sells out the quickest and there are only three non-reserved cars, so it is best to get a seat reservation in advance on these trains. The Hikari, and especially the Kodama, have more non-reserved cars and rarely sell out.
You must have a valid passport and an onward/return ticket for tourist/business visa free stays of up to 90 days. Your passport must be valid for the entire time you are staying in Japan. You cannot work on a 90-day visa free entry.
The Japan Rail Pass gives you unlimited access to all Shinkansen bullet trains except the Nozomi and Mizuho Shinkansen, which run on the Tokaido, Sanyo, and Kyushu Shinkansen lines. The Japan Rail Pass allows you to make a free reservation for these two types of trains, but you still need to pay for the ticket.
Acela trains will reach top speeds of 165 mph (265 km/h) when new trains enter service, and 186 mph (300 km/h) in coming years. Other services reaching 125 mph (200 km/h) are prevalent in the US, and are officially classified as higher-speed rail.
You can get 1 minute or sometimes even more spare time for 1 stop. The indicated allowed speed is 300km/h but the train driver will let it coast to 270km/h or so before accelerating again, to bleed off some extra time.
Overall, it is more expensive to live in Tokyo as a whole compared to Osaka. However, there are higher salaries and price differences in place in other areas to balance this out.
The ideal duration to explore Tokyo is at least 5 days to discover the main areas of the city and the outskirts of the prefecture. To explore Japan's best, spend at least 2 weeks here. Even then, you will realize that there are so many things to discover in Japan.