Hello! Have a big question.
I need configuration like
Shared cart for both shops.
Shared search for both shops.
In search of Shop#1 must be a present products from Shop#2 (like Product3) with Shop#2 URL (like s2.com/goods/product3.html) but not in catalog or direct link of Shop#1.
Summary needs: 2 shops with different templates and domains, different products (but some products are mutual) and shared search/cart/language/carriers/payments.
Are this configuration possible in Magento?
Sharing products from a catalogue point of view is possible across stores in Magento. Note that stock/inventory will also be shared across both sites.
The challenge you'll have is that carts can't be shared across domains because of the way sessions/cookies are managed. If this was a priority you would instead need to create an extension that posted cart contents from one site to the other and the cart was recreated so that carts were synchronised across sites. This is easier for logged in customers but guest customers would have to go through your store switcher code in order for this to work. If they visited the other site manually, the cart synchronisation process wouldn't function.