lavender’s hill free kippu

i see Lavender's Hill Free Kippu and Lavender Free Pass listed in JR hokkaido mail magazine for May 2010 http://www2.jrhokkaido.co.jp/global/pdf/e/ml201005.pdf

However, I cannot find information to these 2 passes anywhere online?

I can find Furano Biei Round Tour Ticket, but I will only arrive Asahikawa by air on 4-jun. Can I buy Furano Biei Round Tour Ticket at JR Asahikawa, and use Ticket B only?

However, I cannot find information to these 2 passes anywhere online?

You did already and provided the link above! The PDF file you linked is the official newsletter of JR Hokkaido, the company which sells these tickets. Just trust it! If you don't, here is the official information also in Japanese:
http://www.jrhokkaido.co.jp/network/kipp/c_3.html

The reason why there is not much information elsewhere is because it is brandnew information.

I can find Furano Biei Round Tour Ticket, but I will only arrive Asahikawa by air on 4-jun. Can I buy Furano Biei Round Tour Ticket at JR Asahikawa, and use Ticket B only?

It seems that there is no version of the ticket for use from Asahikawa. It alwasy includes the round trip between Sapporo and the free area.

Asahikawa is in the free area, so she can use only ticket B (from free area to Sapporo), don't need to use ticket A first (from Sapporo to free area). Am I right?

Ticket A and B are always sold as a set. It is not possible to buy only one of them.

i only need ticket-b (unlimited travel in free area & one-way to sapporo), because it will be cheaper compared to all the single tickets i need for asahikawa-furano/biei/bibaushi trains and i will be travelling these areas for 2 days, before going to sapporo on the 3rd day.

i dont mind not using ticket-a, unless there is a condition that ticket-a must be used first, before ticket-b can be use?

Yes, ticket B should be usable even if you never use ticket A.