1- It is recommended to disable synchronization in most cases. Synchronization is disabled by default in recent IOS releases. If synchronization is enabled, IOS will required a prefix learnt via iBGP to also be learnt via the IGP before it can advertise it to an eBGP peer.
2- Unlike ospf external routes, eigrp external routes are redistributed in BGP by default.
Hope this helps,
Regards,
Harold Ritter, CCIE #4168 (EI, SP)