Importing database: Duplicate entry 'X' for key 'PRIMARY'
but removed all "DROP TABLE" stuff to be able to import it to empty database 


That's where you went wrong. Leave the database dump file exactly as it is, and then import it.

mysqldump adds DROP TABLE IF EXISTS by default, so unless you've specifically told it not to do that, the changes you're making are redundant, even incorrect.

It's a good idea to truncate the cache_* tables before running the data export. That way you don't get lots of ephemeral data in your backup, and exports/imports are quicker. I don't know if it will solve your current problem (if you have no duplicate errors elsewhere in the SQL script then it probably will), but either way it's a good habit to get into.