As a front end developer, do you need to have the skills of Back-end development?

You dont need Back end dev skills as a front end developer. But knowing the basics of back end dev will help you debug out problems which a pure front end developer can't easily resolve. Also you will know how the entire system works as a whole. I say this because I am a front end developer with pretty decent back end skills.

Nope, I am fullstack developer

no you don't, just focus you on the front end development you have many languages and framework to get expertise in such (html,css,javascript,jquery,bootstrap) these are the necessairy one and then you can go ahead for one of these ones (angular, react, vue ) because in the most professionnal job they require one of them

No you don't.

but i think, know something for anything else is a good practice.

no its not need having skills of back end for front end , but back end develpers you must have skills of some basics front end developing

It is important in this area to have a background on the different skills that exist within areas such as 3 types of development: front end, back end and full stack.I believes that building an integrated project is often done by a team, so it is best to focus on skills of finding each niche areas , and so as front end development not necessarily have need skills of back end development.

You just need to have minimum knowledge and the full understaning of the web developement at all but you have to be experienced with the APIs and Ajax  

No , not compulsory. But it will make your life a lot easier if you know the basics of Back-end.