Physical reality appears to prefer the dimension of the quaternions. It is a 1+3 dimensional number system and it is the most versatile division ring.

See:https://en.wikiversity.org/wiki/Hilbert_Book_Model_Project

Size quantization is important. The discrete spectrum. And that depends on different factors. For example, electron effective mass determines the electron spectrum. If it is small, the quantum dot could be large, of order of tens nm.   

No answer is possible without definitions. This matter is far more difficult than your two sentences.

What is the length of a liter of milk ? So on...

Diameter is approximately 10-100 atoms corresponding to 2-10 nanometers. Near the upper limit of size a quantum dot may contain a few million atoms.

Optoelectronic properties of a fixed material vary with the size of a quantum dot. For smaller sizes (2-3 nm), they emit at shorter wavelengths whereas quantum dots of  larger sizes (5-6 nm for example)  emit at larger wavelengths. Properties of quantum dots are intermediate between bulk semiconductors and molecules. Because physical properties of quantum dots are tunable by humans, quantum dots have found a wide range of applicability.

I would say quantum dots are defined as having a size significantly less than, or perhaps comparable with, the inelastic scattering length. So it depends on how large you can get this length to be. Among other things, it depends on the temperature, and it is very hard to get temperature to be very low. So we do not, at present, have quantum dots a cm long. But I do not think this to be *in principle* impossible. It might require a substantial part of the annual US budget to achieve, however, and so be practically impossible.