Do I need JR pass and when to activate?

Hi,
Your best value would be a 7 day pass, used to go down to Kyoto and Hiroshima, then back to Osaka. You can use the pass for Days 4-10. I'd also say 3 + days is way more than you need for Osaka, so to add value to your trip even more, on Day 9 or 10 you can go see Himeji, with Japan's finest castle. I'd also recommend you take at least half a day to see Nara as well. In Nara, the Todaiji Great Buddha is an extraordinary place, as well as many other historic temples, shrines and gardens in the area.

To get from Narita, the 1000 yen bus is a great and cheap way into town, and a 2 or 3 day subway pass for Tokyo can save money too. For Hiroshima, you can use your JR Pass for the loop bus.
To get around Kansai and for the Haruka train to KIX, you might consider the Icoca & Haruka discount ticket.

Good luck.