Are 700 x 28 , 700 x 32 and 700 x 35 tires interchangeable?
You can (theoretically) mount any 700x(something) tire on any 700c  (ISO 622) rim. However, you need to make sure the frame (and brakes if rim brakes are used) can clear the tire without rubbing. 

You generally want to match the rim width to the tire though -- too narrow or too wide of a tire on a rim can lead to tire/rim damage or bad handling.

In your case, the rim width is 17 mm and the chart linked above says 25-37 should all be fine.

As for overinflating, why would you overinflate? You will use a higher pressure with a narrower tire, but overinflating means putting too much air in. And this can be bad for the rim. The right tire pressure is not whats written on the sidewall of the tire -- in fact, you'll almost never use that much pressure. We have many questions on tire pressure setup, so I encourage you to use the search feature to look at some of them.