A responsive design is a key to mobile first design approach. With increasing number of users transacting and browsing on small/smart devices, it is imperative for a website/web store to be optimized for increased goal conversion on smart phones and tablets.
There are varying degrees to which you can enable/implement localization/internationalization. In simplest form, you can use google translate to translate page in multiple languages. This is far from perfect approach. Alternately, a multi-language enabled website will allow you to enter translations. There is more to it than that. What about text in graphics/images? Same thing applies to currency. In simplest form one can convert currency from USD to local current using a conversion rate. But for a global company, the price at which you may want to sell in US market vs Europe may be different. The taxes/VAT may be different. UK/Europe stores display prices including VAT. To summarize, for a good implementation, consult a localization and internationalization expert.
Abandoned Cart Management
Search is a very important function of any web and mobile app project. Depending on the nature of the project emphasis on search needs to be implemented. For example for CMS sites search all content not just pages, post but also all custom objects. If it is an eCommerce implementation, then in addition to searching product catalog, static content and blog; we implement predictive/type ahead search, weight based/weighted search, etc.