May I use BizTalk Server 2013 R2 Enterprise with a Visual Studio Enterprise with MSDN subscription on test and development devices during the contract period?

Yes, you may. For this purpose, Microsoft provides a comprehensive overview, which can be obtained from the following link.

For confirmation of the BizTalk Server 2013 R2 Enterprise, see line 110 of the table. The current version of this overview (July 2016) is attached to this Use Case.