Is the length of time, say months, for each season the same all over the world or can it vary?
As has been noted in a comment, it depends on how you define seasons (see https://earthscience.stackexchange.com/a/2603/111).
If seasons are defined in astronomical terms, then they have the same length everywhere on the planet. This is simply down to geometry.
However, the effects of astronomical seasons vary geographically in a number of ways. The magnitude of seasonal changes, for example changes in day/night lengths, is more pronounced in higher latitudes, so the effect of (for example) winter might be noticeable for a shorter time period in the tropics than the arctic, and hence some people might reasonably consider winter to be shorter there. There are other, less systematic variations that depend on local climate and weather. In weather terms, not everywhere in the world has the same 4-season cycle that temperate zones tend to experience - so when defining seasons in terms of observable effects one often has, for example, a wet season and a dry season rather than spring /summer /etc.