what happens if the manufacturer recomends15" tires and one uses 14" tires and rims for snow tires? Will it harm the car?
It depends. If the wheels are designed to fit the car you should have no problem. The wheels must clear the brakes and fit correctly. Many cars have different wheel sizes depending on option packages. In most cases any wheel that is optional for the car will fit. The smaller diameter wheel will probably take a higher profile tire to even out the diameter of the wheel/tire package.
There are exceptions to all this. What car are we talking about?
Google tire size calculator and then make sure that the OD is the same or within 1%.
You are referring to the rim diameter, not the tire diameter. It is possible to use a smaller rim on a car if it fits. As Wha said, you need to be concerned about the outer diameter of the tire. As an example, a tire for a 15" rim with a narrow sidewall could be the same diameter as one for a 14" rim with a wide side wall. You also need to make sure that the tire width fits within the wheel well. If it’s wider than the 15" tire, there could be problems.
It is hard to say. There are several factors.
Rim diameter does not mean it will fit there is also offset, bolt pattern and type of rim. Make ssuree the rim is listed for your car.
Since different tyres will fit on different rims (the inch size refers to the rim diameter and nothing more) you may well have a tyre that has the same diameter size and yet not properly fit the rim (rim may be wider or narrower) and the distance between the rim and the outside of the tyre can be different. Generally you want a tyre with the same outside diameter.
You also want to make sure any tyre you use meets the weight rating and speed rating for your car.
Winter tyres (they are not snow tyres any more and winter tyres are better for most uses than the old snow tyres) are usually more effective is the tread is not as wide as standard.
All this is usually taken care of by the tyre dealer. You can find a lot of information shopping on line. I used TireRack and I feel I get a good deal and they had all the size information right.