Can you support 2 prices per product, i.e. member price and non-member price based on member ID?
Yes, there is a member price field in the product setup screen and also a checkbox called show member pricing in the cart admin settings. See page 46 of the cart users guide http://www.smith-consulting.com/Portals/0/docs/smithshoppingcartmanual.pdf
Show Member Pricing - When the show member prices checkbox is checked the member pricing will be displayed to the user in the your store on the product lising page, product detail page, cart and confirmation screens. The member prices are displayed alongside the regular prices defined for your products. The member pricing is defined in the product setup screen.
Is possibe to change the "member pricing" label?
Yes, you can modify the productlist.ascx, cart.ascx and confirm.asx pages and change the member price label to anything you want.