Once they are mounted on the vehicle and aired up to the correct pressure, yes they should be round. If not, the tire is defective and must be replaced.
Fling them away and get new ones.
Well I think you should change your tires to triangular blocks of wood and see how that goes.
Buy new ones! Out of round tires is a defect in the tire. Demand that the place that sold you the tires replace them. I am assuming you have not slammed on the brakes and slid the tires far enough to flat spot them. Tires can be shaved to make them round again but doing this causes a loss of rubber and they will wear out sooner.
Tires are made for the conditions that they are driven in. Therefore if you live in an area that has cold winters, that is it snows for a large portion of the winter, you probably should purchase winter tires. If you are living in Florida for example winter tires would not be required and year round tires would be sufficient.
You sould have the new tires mounted FIRST, then have them do the alignment at the same visit.
In my opinion the new tires go up front. The steering tires need the grip.
You should check to see if your tires are bald and are not durable anymore.
After
Yes, you should have balanced all 4 tires.
If you are wondering what criteria has to be met when shopping for new car tires because you are considering on buying new car tires for your car, then you should follow the easy guide for picking out tires for your car.
The new tires should be placed on the rear axle to lessen the risk of hydroplaning.
All tires should be balance checked before being placed on a vehicle. If the tires are not balanced it will cause uneven wear and they will not last as long as they should.