You will be understood but semantically it doesn't make sense. Essential is absolute, it can't be compared. It is either essential or not essential / nonessential / inessential / unessential. If you worked for a newspaper your editor wouldn't allow it. Importance is relative, some things are, or can be, more important than others. They are not absolute, they are comparitive. Short answer: You might hear people say and it's understandable, but technically incorrect. I suggest comparing with important instead.

You can say either, both sound correct. The most essential thing means the same as saying the most necessary thing.