Those who call Shinkai the new Miyazaki are blind. Shinkai seems to try very hard to fill the master's shoes in this movie (what with the whole Shinto temple in a magic meadow), but his approach falls squarely in the "anime was a mistake"-category. Those who think that a movie using Jpop-infused montages can in any meaningful way be compared to Miyazaki, simply doesn't understand why he is the master of his craft.
A comparison that is often made regarding Makoto Shinkai is that he is this decade's Miyazaki. I don't believe that but what I certainly do believe is that 'Your Name' is a film that puts Shinkai into a league of his own. At times the film can be narratively confusing but the journey that it takes you on will leave you on the verge of your seat and desperate to reach out onto the screen. It makes you feel human.
3-4. Reflexivity is one of the biggest stars of the movie. The way sequences opening the film gain extra meaning as more context is revealed serves as a nice complement to the unexpected time-travel component buried in the 'Freaky Friday' setup. What's especially noteworthy is how many resonances with Japanese culture the varies links to past and future attain. Very impressive in that respect, overall.