I'll answer these questions out of order:
Similarly, what does the set of questions measuring a construct mean? Does it mean that the questions are mutually exclusive or do all the questions are to be used together (mutually inclusive) to measure the underlying construct?
Imagine that you want to measure someone's innate ability to learn languages. That isn't something that you can observe directly. However, there might be several questions or tests availble that people think reflect this ability. But do they?
Alpha is a measure of internal consistency reflecting the variation that is shared in a set of observed variables. If a set of observed variables (e.g your questions or tests that supposedly reflect language ability) share a lot of variation, it might then be reasonable to interpret them as all reflecting some shared, underlying cause that you cannot (or have not) observed directly.
The reason for asking multiple questions about the same underlying, unobserved construct is that their individual errors will (hopefully) be indepdendent (and kind of cancel each other out - though this is a simplification), helping you to focus in on the variation that is shared. This can be more formally tested with the appropriate latent variable model (latent trait, latent profile, factor analysis, latent class).
Do we have to use it in sample survey before going for final survey? or is value of Alpha calculated based on the final survey data?
Once you have designed an instrument (some set of questions intended to measure the same underlying contruct), you should evaluate it during the pilot phase and make any neccessary adustments before applying the instrument more widely. You would then also evaluate the psychometric properties of the instrument (including alpha) in the full, final sample.