I can just enable work order object under Setup --> Field Service Settings but not all objects that comes with Field Service lightning. We got Service cloud license in our org.Do I still need to request Salesforce to enable field service in sandbox ?
Yes you need to ask Salesforce. Please see the details here https://help.salesforce.com/apex/HTViewSolution?urlname=How-to-activate-install-Field-Service-Lightning&language=en_US
Field service lightning (FSL) and service cloud operates on different pricing models. The licenses for FSL is further separated into licenses for field agents, field dispatcher, field mobile agents and contractors. If you do not need to the skill and routing features of the FSL, you may also have a look a Lightning Scheduler which is an on-demand appointment reservation.
The updated pricing for each licenses can be found here: https://www.salesforce.com/ca/products/field-service/pricing/
The features for each licenses can be found here: https://www.salesforce.com/ca/products/field-service/features/