exists currently any way, how to communicate with PostgreSql database, when I want to use ASP.NET vNext? I'm looking for solution, which will work mainly on linux.
EF7 supports only MS SQL a SqlLite now and Npgsql isn't ported for ASP.NET vNext.
Instead of EF7 you can use NHibernate together with Fluent NHibernate. Npgsql is also working well on ASP.NET 5 (vNext) on Linux. Here is a complete example of ASP.NET vNext application with NHibernate + PostgreSQL working on ubuntu server.