1)Apart from the meaning "come", "来" is also a direction, meaning "towards me/to me". The sentence doesn't mean "mom often comes by calling", which makes no sense in either Chinese or English. Yes, it is the same as "妈妈经常给我打电话".
2)Yes. This is the correct interpretation. But there should usually be a purpose when someone calls around, either trying to organize something or to find some information. You need to specify it in the sentence so people would know mom isn't crazy.