is it possible to set engine for database (not the tables)?
There is no "database" engine setting. A database can have tables using different engines.

There are two variables that define which engine will be used when a table is created with a CREATE TABLE that does not include an ENGINE = EngineName specification. The variables are the (global and session) default_storage_engine. The global is configured at startup (from my.cnf or command line) and the session variable can be setup during each session.