JR Pass during Golden Week

Hi everybody,

My wife and I are planning our trip to Japan. We are coming from California. We were in a hurry to plan and unfortunately did not realize we were arriving during Golden Week. We were able to book our flights and hotels though so we're good there. Now we're concerned about getting to the places.

So we're staying from April 30th to May 6th. We're arriving in Haneda Airpot. Here is when we think we'll be using the JR Pass:

Sunday, April 30th- Arriving in Haneda Airport at 12:50 p.m. We are planning to take a train to Kyoto. My wife has booked two nights at the Hyatt there.

Tuesday, May 2nd - Leaving Kyoto at night to Tokyo.

Thursday, May 4th - Going to Mount Fuji so going to Odwara and buying the Hakone Free Pass.

Saturday, May 6th - Going from Tokyo tto Haneda Airport

So here are my questions:

1) I saw that people recommend you make a reservation before Golden Week or else you won't get a seat. However if I'm arriving right on the Sunday of Golden Week, how can I guarantee a seat? Will this mean that me and my wife will have to hope that seats are unreserved to Kyoto?

2) Is it worth getting the Green Pass? Since it's Golden Week, I'm guessing it may be so packed that I won't be able to get into a Green Car during a certain time and that would mean I would have to wait until a Green Car is available?

3) On the first day when I get the JR Pass, am I able to reserve for my trips from Kyoto to Tokyo, Tokyo to Odwara, and then Tokyo to Haneda Airport?

Thank you all in advance for any help.