Yes you can put a range under a window.
Most building codes don't have any restrictions on where you can place a stove or range and putting the range or stove under a window is perfectly fine although the window may get grease built up on it.
But if it's warm out and you're cooking on the stove then you can open the window to let smoke out or fresh air in.
You can also install a range hood if there's room even if you have the stove in front of a window.
Range Hoods don't come with plugs and instead the range hoods have to be hardwired.
So you need a wire to wire the range hood too.
However you could hook a big enough cord to the range hood if you want too and needed to plug it in.
A range hood works by use of a fan that pulls the smoke and other smells out of the kitchen.
The fan creates a vacuum to suck the smells and smoke out of the air above the stove and send it outside.
A range hood is a device that mounts over the stove or range to help remove cooking smells and smoke from the kitchen as you cook on the range.
The range hoods job is to remove airborne grease, combustion products, fumes, smoke, heat, and steam from the air by evacuation of the air and filtration.
Although you can use a stove or range without a range hood the range hood is a good idea to keep your kitchen and homes air quality good.
A range hood keeps cooking exhaust, chemicals, and smoke out of your kitchen.
It improves your indoor air quality and streamlines your cooking experience.
Range hoods are made to improve the air quality of your kitchen after cooking.
They remove odors, grease, smoke, and fumes produced by using your stovetop.
The appliance sucks up the polluted air and filters it (as with a ductless model) or is carried to the exterior (with a ducted model).
Range hoods do not have to be vented to the outside.
But, ducted range hoods are almost always preferred over ductless hoods.
They remove all the smoke and cooking exhaust from your kitchen, while ductless hoods recirculate your cooking exhaust back into your kitchen.