Q: Is it necessary to have a cooling fan within a laptop?
A: Yes, it is necessary to have within. It is like someone asking, is it necessary to have air condition or engine in a flight? :)
Q:Is it Ok to buy if it does not have a cooling fan?
A: It is always better to buy a laptop that has an internal (or inbuilt) cooling fan or at least the new technology invention to prevent from the laptop heating.
Q: If we buy a separate cooling pad device on which to rest the laptop, would that help?
A: External cooling pad really helps additionally to cooling the laptop from the heat and extend the laptop lifetime, of course.
Note: In general, one can use laptop while charging and no issue on its heating, in fact it shall not heat upon (that indicate the sign of a good condition laptop). If heating while charging then there could be some other issue like internal (default) cooling fan is not working or some other (like processor) or motherboard issue or dust blocking near or within cooling fan area or maintenance required soon etc.
One can't compare the laptop against smartphone on heating issue though both of them have more or less similar features, electronic gadget and technically few gadgets among may match this issue.
The laptop charger and the laptop shall not have anything covered outside which stops air flow and ventilation etc.