Is using innodb_file_per_table improve speed of alter table command?
innodb_file_per_table is convenient option to manage disk space used by innodb, but it won't improve ALTER TABLE time.

As of 5.6 InnoDB supports online DDL for some kind of ALTERs. Check Online DDL page to see what's currently supported.

If not, you may consider using pt-online-schema-change or similar tool(https://github.com/github/gh-ost, https://github.com/facebookincubator/OnlineSchemaChange). It will run long time, but won't block the table.