Hokkaido Itinerary

Hello everyone, I need some help on planning my itinerary. I bought a ticket to Hokkaido for my honeymoon on April 29 to May 9 2018, and then I learned that I traveled during golden week, the worst time possible.

Here's my rough schedule, and I'm gonna add more details after I'm sure of my transport options:
April 29: Arrived at New Chitose Airport around 8pm, activate my JR pass and book shinkansen to Hakodate.
April 30: Going from Sapporo to Hakodate
May 2: Leave Hakodate in the morning to Asahikawa
May 5: Leave from Asahikawa to Sapporo
May 5 - May 8: Sapporo and Otaru
May 9: Going home

My question is
1. Is it possible to activate my JR pass since I arrived pretty late at evening?
2. Can I book a shinkansen to Hakodate for the next day immediately or should I stay for a day around Sapporo?
3. I heard that on golden week, you can only book shinkansen for tomorrow's trip. Is it possible that I would run out of seats for tomorrow's booking?

1. Is it possible to activate my JR pass since I arrived pretty late at evening?

Unfortunately your arrival is too late:
http://www.japanrailpass.net/en/exchange.html

2. Can I book a shinkansen to Hakodate for the next day immediately or should I stay for a day around Sapporo?

Unfortunately no shinkansen for Hakodate from Sapporo.

3. I heard that on golden week, you can only book shinkansen for tomorrow's trip. Is it possible that I would run out of seats for tomorrow's booking?

Unfortunately you received wrong information. Again, unfortunately no shinkansen for the places you are visiting.

As previous poster said, there are no Shinkansen in Hokkaido beyond Shin-Hakodate.
I am not sure which JR pass you are talking about, but doubt that the full one will pay of for your itinerary. Have a look but I think a Hokkaido only pass does exist. Also as you seem a bit lost with your train connections, just look them up on google maps or similar to get a feeling for the transport time needed. Trains in Hokkaido are quite slow.

For the first night, I wonder why you go to Sapporo if the next day you go to Hakodate. Either stay in Chitose or consider a night somewhere in between Chitose and Hakodate, eg an onsen place.
Onsen and Biei/Furano seem to be missing from your list of destinations.

If car rental is an option, consider that as Hokkaido is about seeing the countryside, so public transport is not so convenient.

Enjoy your honeymoon in Japan!

Unfortunately you received wrong information. Again, unfortunately no shinkansen for the places you are visiting.
My bad, I automatically assumed the trip between the cities use shinkansen because they are far away, and this is my first time in japan so things are a bit confusing to me.

So instead of using shinkansen, we'll use ordinary trains without any bookings necessary then?

For the first night, I wonder why you go to Sapporo if the next day you go to Hakodate
This is because of my assumption that we're gonna use shinkansen, and I heard that we need to book a day before to use shinkansen in golden week. I'll just stay at Chitose and go to Hakodate the next day.

Onsen and Biei/Furano seem to be missing from your list of destinations
I do plan on visiting Biei/Furano, but I think I'm gonna stay at Asahikawa and do one day trip to each places. The itinerary above is still very rough because I'm still planning for my hotel accommodations around those places, and flesh out the details after that.

If car rental is an option, consider that as Hokkaido is about seeing the countryside, so public transport is not so convenient.
Car rental would be much more expensive so I think it's not an option for me :(

So here's the updated itinerary:
April 29: Arrived at New Chitose Airport around 8pm, stay at Chitose.
April 30: Activate Hokkaido Rail Pass and immediately travel to Hakodate.
April 30 - May 1: Travel around Hakodate city and Matsumae Castle.
May 2: Leave Hakodate in the morning to Asahikawa.
May 2 - May 4: Travel around Asahikawa, Furano and Biei.
May 5: Leave from Asahikawa to Sapporo.
May 5 - May 8: Travel around Sapporo and Otaru.
May 9: Going home.

Questions:
1. I plan to stay only at the major cities, and travel to the countryside using trains every day. Is it a feasible plan? Or do I need to book hotels at the countryside?
2. In Google Maps, as long as the tracks marked with JR, the costs would be covered by Hokkaido Rail Pass right?

Enjoy your honeymoon in Japan!
Thanks :)