Hokkaido in Early May 2018

Dear all, my first trip to Hokkaido will be from May 6th to May 16th

1. I planned on taking a train straight from Chitose Airport to Hakodate. Spend maybe a night or two and then head to Sapporo. Please advice on how to.

2. Will I be able to see cherry blossoms, lavenders, tulips, etc at this time of the year? Should I rent a car and self drive to outskirts like Biel, Blue Pond, etc? Please recommend a route

3. I just realized that May 6th is the end of Golden Week. Will I face any problems with transportation from Chitose to Hakodate?

Sorry, I havent done any homework on Hokkaido. Hopefully you can recommend a itinerary for me.
Thank you all for your help :)

Train from Hakodate to Sapporo:

http://www2.jrhokkaido.co.jp/global/english/train/

I havent done any homework on Hokkaido. Hopefully you can recommend a itinerary for me.
......Welcome to Hokkaido.Not only Japanese national but also thousands of Foreigners love to visit Ainu village,odori park,Moerenuma park,panoramic view from SapporoTV tower.Hokkaido Museum of Modern Art, Museum of venetian art & Sapporo Beer Museum,kitaichi glass Factory are worth to visit.One of My favorite place is Mount Tengu.If you visit this place,you must ride cable car in otaru Tenguyama Ropeway.

As for cherry blossoms, it's never the same and can differ from year to year, but you might be lucky:
http://zoomingjapan.com/travel/cherry-blossom-spots-in-tohoku-and-hokk...

As for self-driving, I'd recommend it.
Here's my summer vacation (2 weeks) in Hokkaido where I was mainly driving. Maybe that can give you an idea of possible routes:
http://zoomingjapan.com/travel/hokkaido-in-summer/