Cost Comparison (7 Vs 14)

I have my itinerary roughly planned for a 12 day trip in Japan -

Day 1 -4 / Tokyo
Day 4-7 / Osaka (Day trip to Kobe)
Day 7- 10 / Kyoto (Day trip to Hiroshima)
Day 10 - 11 / Hakone
Day 11-12 / Tokyo

Now the question is to purchase a 7 day pass or a 14 day pass.

i think i might be able to get around with just a 7 day pass instead of 14. I'll activate it on the way to Osaka (Day 4) and it should last me till my trip from Kyoto to Hakone (Day 10) right?

Do I need to tell them a specific date for activation when I pick it up or is it just whenever I start using it?

From there to return to Tokyo I would take the Romancecar and while to/from Narita i'll use NE'X and any travel in Tokyo i'll use the Suica. This should save me some money compared to getting the 14 Day pass given that the timing of all this works and it doesnt expire before I leave Kyoto.......Is this plan reasonable?

My cost break down on the difference between the 7 and 14 day pass should offset the cost of paying for each of the services outside of the 7 day pass (NEX, Tokyo metro and Romancecar) unless there are any other costs/fees I missed.

Also, for Suica card - does the money put on to the card work on all lines in Tokyo? Can it be used for the transport system in Kyoto and Osaka?