Is it compulsory to pick only a region pair as Azure DR region?

Certain Azure VM types (like some in G & M series that I require) are not available in the Azure region pair (US East, US West).

Will there be any constraints on functionality if I choose an Azure region other than the Azure region pair (say, US East 2, US West)?

Azure makes certain guarantees about region pairs including that it will not upgrade a service in both regions simultaneously. This allows users to architect HA/DR solutions that use both regions and which can there survive an outage in one region. Deploying services into non-paired regions such as eastus2 and westus2 does not benefit from this - and theoretical could subject services to simultaneous upgrades of underlying infrastructure.

In cases where users want to benefit from pairing and a specific VM size is not available then an alternative VM size would need to be selected in the secondary region. This assumes the application has been architected to use both regions.

Will there be any constraints on functionality if I choose an Azure region other than the Azure region pair (say, US East 2, US West)?

Based on my knowledge, there are no constraint on functionality if you choose the two location. US East and US East 2 are two data center and they are all in Virginia. Please refer to this blog:Tips for Choosing a Microsoft Azure Region.

If possible, you could select US East 2 and US West 2 as a pair. The two locations all provide G series VM. But for now, M series VM is not provided on US West and US West 2.

Also, based on my experience, G and M series VM will come to EAST US in the future.