"Mom speaks softly to me."
Translation:Ibu berbicara dengan lembut terhadap saya.
Yes, that's how I use it myself.
In the other sentence it's used to refer a specific dancer, 'si penari'.
You can use it to refer to a person whose name you don't know.
There is also a sentence where it's used to refer to a person you already know, something like this I believe :
'si Tono anak yang baik'. = 'That Tono is a good kid'.
In that sentence it's used as a dimunitive.
It can be used like that when you refer to familiar people/friends.
I also use it to refer to my pet:
'si Happy gembira banget.' = 'Happy is very happy.'
(Happy was the name of my dog).
It can also be used to 'nickname' people.
'si Gendut' = the fat one, fatty
'si Gundul' = the bald one, baldy
'si [whatever]' = the list is endless....
Maybe that's why I never use 'si' to refer to my (or somebody else's) parents ☺