Is it possible for a physical object to be four-dimensional? This depends a bit on what you mean by a "physical object". But it seems plausible to say that the could be a four-dimensional world with four-dimensional objects in it, and why should we not in talking about such a possible world call such objects physical objects? I would address your question in the same way. There could be a one-dimensional world, and there could be objects in it. Again, it seems plausible to say of these one-dimensional objects that they are the physical objects of that one-dimensional world. But then again, if someone where to feel very strongly that the expression "physical object" should be reserved for three-dimensional objects, I for one would not want to get into a long argument over this point. Now another question you may have in mind is whether there can be one-dimensional objects in our three-dimensional space. We can certainly describe such objects geometrically, so they are possible in this sense (and,...

The in/at variation is a convention of the English language and has no equivalent in many other languages. It seems to mark no significant underlying distinction, and your question is then one about proper English. Understood in this spirit, I would say that you are both right. With some places we use "at", with others "in". Consider two buildings, for example, my school and my house. One could say that I am in the first building or at school. And one could say that I am in the second building, or in my house, or in my home, or at home, or at my place. I assume a grammarian could give you a general rule about when we use "in" and when "at". But, as my example shows, this rule cannot draw on the type of location alone.

With regard to both questions, I understand you as imagining that objects are longer or shorter in all dimensions (not merely in one dimension). So spheres would still be spheres, except larger or smaller ones. Right? On your first question, this is not possible if we hold fixed the laws of nature holding in this universe. To illustrate: In your Twin Solar System, scaled up by a factor of 2, Twin Earth would have eight times as much mass, and gravity near its surface would be roughly twice as great (surface gravity is proportional to the planet's mass divided by the square of it radius). Like the Earth, a scaled-up object would have eight times as much mass, so the gravitational force acting on it (its weight) would be 16 times greater. Now imagine this object suspended by a string. This string would be thicker in two dimensions, hence four times stronger. But the object's weight would be 16 times greater! So, on Earth, the string may be sufficiently strong to support the object even while on Twin...