How can every atom have unique spectral lines?
Do all noble gases or alkaline earth metals have similar spectral
  lines considering the above points?


The question is interesting after you modified it. The basic set of reasoning you provided is the main story. Each element has a different nuclear charge and the outermost electron(s) is responsible for the atomic emission spectrum. Since the nuclear charge is different, those outermost electrons experience a different potential energy. Their kinetic energy is also different from element to element. 

The key question is what is meant by similarity? The atomic spectra of all the elements is visualized as bright lines on a dark background. The reason they appear as lines is just because of the instrument used to observe the atomic spectrum. There is nothing fundamental in the "line"spectrum. The atomic emission appears as lines because the slit in the monochromator is shaped like a very narrow rectangle. This is the image of the slit. If I made a very narrow circular opening, the images will appear as bright points rather than lines. Consider that line spectrum is the conventional way of looking at the atomic spectrum.

For the visible region, let us look at the visible spectrum of alkali and alkaline earth metals.



or look at the visible spectrum of noble gases



Are they similar in any way? Visually there is no similarity at all in the spectrum. Look at the spectrum. The reason we cannot see any similarity is because the dispersion of the lines is on the "wavelength" scale. However, very bright, I mean really genius spectroscopists of the 18th and the 19th century were able to find out a patterns (or call it as mathematical series). They figured out that each set of lines forms a pattern as Sharp series, Principal series, Diffuse Series and Fundamental series and there they found similarities in patterns-in terms of mathematical series. In short, our eyes cannot interpret those series. Another complication arises because we are just looking at the visible region. There is a ultraviolet region and then there is an infrared region. We cannot see it without using more sophisticated instruments.