Yes, all three forms are fine. They're only different in terms of formality/ casualness. For a learner, it's safe not to omit too much or people may fail to understand you. So, my advice is to stick to 一点 as the minimum.
儿 is only the rhotic accent of the word. You don't have to pronounce it if you are not used to.
And yes, 一 can be omitted. 有点 is idiomatic too.
In English you can say “a little bit / a little / a bit”, the case is as flexible as this.
Although not as common, I think some people do say these in some circumstance. Of course they are correct too, just a little bit redundant to Beijinger's ears.
More frequently, they appear as written language.