Suggestion for Shikansen vs. JR Pass

I learnt from your forum that JR Pass and Shinkansen are in fact two different types of tickets- Is this correct?

My itinerary is as follows:
30-Mar Reach Tokyo
31-Mar Tokyo
01-Apr Tokyo
02-Apr Travel to Kawaguchi
03-Apr Kawaguchi
04-Apr Travel to Kyoto
05-Apr Kyoto to Nara day trip
06-Apr Kyoto to Himeji day trip
07-Apr Kyoto
08-Apr Kyoto to Hiroshima to Miyajima via ferry
09-Apr Miyajima
10-Apr Miyajima to Hiroshima to Tokyo
11-Apr Tokyo
12-Apr Tokyo
13-Apr Tokyo

Can you please suggest which ticket would be the best option for us to buy budget-wise? Can JR Pass be used for city travels internally? Or do you suggest buying local subway pass to travel internally?

Is Shinkansen different from JR Rail?

What are the blue vs. green lines in JR rail?

In the season of cherry blossom would it be possible to get tickets over-the-counter or do you suggest we buy them in advance?