Ramp current in inductor
When DC voltage is applied across an inductor, would the current through it be ramp? 


Yes


  Is this practically possible only when there is no resistance connected in series with inductor?


Yes, or low enough resistance to not affect the result much. Remember that all real inductors have parasitic series resistance, so being able to neglect a small resistance matters.


  Why would the current through inductor be ramp in this circuit of dc-dc buck converter?


The capacitor C should be large enough to prevent \$V_o\$ changing very much.

Of course the output voltage is not perfectly constant. There is always some voltage ripple in this circuit. So the inductor current is not a perfect ramp. But if it's designed reasonably, it will be close enough to a ramp to do useful analysis with that approximation.