Why do my pedals shake and pop? I just purchased a cruiser bike online that I had to assemble. 

When I rode it for the first time, I notice my pedals felt shaky, whether pedaling or coasting, and when I did pedal every few seconds they made a crack/pop.  I don't feel anything abnormal when this happens. 

Turned the bike over, and I noticed the chain shakes too. It is tight, but the wheel looks as if it is up as far as it can go- it looks like if I adjusted it further to loosen the chain, I'd be at risk of it falling off. 

I opened up the wheel sprocket- no broken ball bearings

Does any one know why this is happening, and if its an easy fix or defective bike that I need to return?
The popping sound could be coming from the chain not lineing up properly on the freewheel. This can happen if the chain is either bent and or twisted or if the chain is not the proper size for the sprocket. More than likely it is a bend or twist in the chain.