The answer to both of your questions
1. Time zone must be the same (Honestly, I have not tried doing this on different time zones settings since this is a simple per-requisite)
2. You just need to install the DB on the primary node and during installation of the heartbeat, the process will take a NT_Backup of the system. So when installing HB on secondary, the process will take the backup over CIFS and restore thus you will see the DB "restored" on the secondary server. That is also the reason why they require you to PHYSICALLY remove network cables from the secondary server when the restoration process ends.
Good point to note is that before HB installation on primary, make sure your OS is patch to the level according to your company's policies for your primary server.