Can I use mysql/mariadb databases on different OS?
Check out the manual here. However, if you're transferring between 32/64 bit, then you'll have to use mysqldump, see here which gives you a text-based dump of the SQL statements you'll have to run to install your database. The commands for mysqldump vary according to whether you're using MyISAM or InnoDB, so just be aware of that.

On Linux, there are more tools available than for Windows - personally I would recommend Linux - you have mydumper (an enhanced replacement for mysqldump) as well as backup methods which aren't available on Windows such as Xtrabackup from Percona (free Open Source hot backup programme for InnoDB) and LVM snapshots. There are many other useful tools in the MySQL ecosphere that ony work (or are far easier to use) on Linux than on Windows. I know that the primary Oracle/MySQL development environment is Unix based (I did read this somewhere, sorry can't remember), either Linux or Solaris.