Trains and cites

Hi, before I buy two JRP I would like to confirm the following.

1. I fly to Osaka from there I will get the train straight to Kyoto downtown
2. After a few days in Kyoto I will like to visit Takayama
3. Then Takayama to Tokyo where I’ll stay for 5 days and will fly home from Tokyo

So question I have does the JRP get me to these cites whiteout any trouble?
Also is it cheaper me buying a JRP to do my trip rather than individual tickets.?
Also can I use the JRP to use the metro around Tokyo?
When I buy online will I get a email confirming my purchase that I just show to collect my pass when arriving in Japan? And this can be done at any station?

Thanks and looking forward to your reply.