The correct answer is number 1. "How often do you go shopping?" she asked her. She asked her how often she went shopping. When you use reported speech you back-shift the tenses, following the rule of "true at the time it was said". This is much easier to understand than trying to work out if the situation is still true at the present moment.

I have used both, but I agree that number 1 is more correct. The change in tense isn't really supposed to be context-sensitive. You just change the tense; it isn't supposed to make sense, it's just the language. He said he liked reggae. I thought you said you were sick. You said you knew the answer. Look up the phrase "asked if I was American", for instance, on Google; it's very common, and being American or not isn't usually temporary. Or "You said you loved me." "She asked her how often she goes shopping" sounds utterly ridiculous if the conversation took place 150 years ago!

Number 2 as per Peachy.

The correct answer would be # 2. She is asking her in a more present way how often she goes shopping. However, to ask her how often she "went" would be referring to how often she went shopping in the past. Hope that helps.

I'd like to help you, but I barely speak in English and I'm working at my pronunciation, too. I'm not a native speaker, maybe someone from USA, UK or Australia would like to have a chat with you. Good luck! :)