Well, literally, “一点儿”has got the same meaning as “一点”. This is the language point of " 儿化音” in Mandarin Chinese learning. Practically, people from middle or southern part of china donot use "儿化音”as much as people from northern China or those from Sichun Province. You can also found such kind of differences between British and American English.

Yes.这是汉语普通话和某些方言中的一种语音现象，即后缀'儿'字不自成音节，而和前头的音节合在一起，使前一音节的韵母成为卷舌韵母。又叫儿化韵。比如“小孩儿”。

The same. People living in some areas of China tend to plus "儿er" after many words. But It's the same radically.

Yep.

Forgot to say that both "yidian (一点）" and "yidianr（一点儿）" mean " some" or " a little bit". "儿化音”is the way that people read some special words with an extra pronouncition of "er". e.g. kids in Chinese 小孩 xiao3 hai2 ------小孩儿 xiao3hai2er ----- xiaohair