Sadly i don't know how to show Picasa albums/photos on Photos section, but for showing them on your group homepage you can use Google Gadget. I don't know will it work also with blog or forum messages, but embed codes for it should be work.

On the bottom of the group homepage is block Add New Block, sadly at moment Google Gadgets section didn't work for me, but i choose HTML Box and used embed code there. And it forked for me, it looked out like this

Embed code can you generate here
http://gmodules.com/ig/creator?url=http://js.hohli.com/photogallery/photogallery.xml&up_user=AntonShevchuk&up_album=DigitalPhotoRu&synd=open&w=404&h=324&title=Picasa+Photogallery&border=%23ffffff%7C3px%2C1px+solid+%23999999

If the link is not accessable, then go for it here
http://anton.shevchuk.name/google/google-photogallery-picasa/

  If it's not that you search and want, then you may find more from following pages

http://www.paulvanroekel.nl/picasa-web-restyled/integrator/

http://www.practicalecommerce.com/articles/2514-How-to-Embed-Photos-and-Slideshows-from-Picasa-Flickr-and-Photobucket

http://picasa.google.com/support/bin/answer.py?answer=66969