Does Google Nexus 4 work in India? I am planning to buy a Nexus 4 from US and want to use it in India. 
Should I expect any issues with this?
Is that phone compatible with all carriers in India?
Are there any power related problems?
Yes the phone is compatible with all Indian carriers. I personally use it on Vodafone.  Side note: Why are you buying it from the US when it's available here? The $200 model is sold out you know.