Arrive March 2, depart March 10

We arrive in Osaka (Kansai airport) on March 2 around 7pm, and plan on staying in Kochi (Shikoku) for most of the trip. Departing Kansai airport for home on March 10 at 8pm.

We are planning on staying near the Shin Osaka station for the night we arrive March 2. If we activate our 7-day JR Pass on March 3, will it be good until we leave on March 10th?

Also, how much does it cost to get from Kansai airport to Shin Osaka station if we are taking a train upon arrival on March 2.

Thank you!