TYPO3 Core

Whenever I try to add e specific product (Flugzeug) to the already filled basket, the formerly products will be canceled and only the new product will be in the basket anymore.
Also when I try to checkout the basket, there is the message "The basket is empty" and no order will be registered and sent to the shop owner.

Can somebody make me an offer to debug/fix it?

Typo3 4.2.10
Shop: tt_products 2.6.2
URL: www.jacqueline.ch
Php: 5.1.2 AND 5.2.11

The developer of tt_products confirmed that tt_products is properly installed and works fine - except the session problem witch is not caused by tt_products.
(issue imported from #M13038)