approximation of a digital signal using the harmonic
I will answer your questions just as they are asked - keep in mind that a thorough understanding of the topic requires careful study of the Fourier series.

A1: You use only odd harmonics because a square wave contains only odd harmonics. Again, the Fourier series explains it quantitatively, but for a qualitative understanding try to see it like this: if you look at the original square wave, you will see that the signal is very fast when t=0, t=T/2, t=T and so on. When t = kT it is rising fast, when t = kT/2 it is falling fast. This same property is shared with odd harmonics, while even harmonics it is the opposite.

A2: Your approximation is on the right path, but some things are not extremely precise. If you want to synthesise a square wave, you do not combine multiple sine waves "in the real world". Seeing a square wave as a sum of sinusoids is useful so that you can estimate the BW you will need to transmit it, for example, or you can understand if some imperfection that you are measuring are there because of the limited bandwidth of the instrument, or maybe come from somewhere else.

Digital signals "do not exist", the world we live in is analog. A digital signal is a mathematical artefact that is useful for a certain type of analysis, so you will never try to approximate a digital signal in the real world. What you can say is that you want to approximate a square wave, and the more harmonics you use, the better your approximation is.