In Conditional Random Fields, is mandatory to use features related to following and preceeding tokens?
In other words, do we need these features related to other tokens?


No, these features are not needed. But they are often useful: CRFs handle sequential dependencies between the labels, however it's up to you to provide the relevant features, in particular some to represent the dependencies between (certain) features if needed. 

With text, this relation between consecutive tokens is very often a relevant indicator. I'd suggest that you try both version, without and with this feature, and you're likely to observe a higher performance in the latter case. In my experience it's often worth trying different combinations, including trying features which go two or three steps back.