还 vs 也 for expressing multiple actions
I think what your Chinese friend said is pretty much right. 

In my opinion, 还 denotes the sense of "further more" or "to a larger extension". Well, 也 connects the two things with the same level of importance, severity, priority and etc.  

E.g. 我喜欢唱歌，也喜欢跳舞. can be simply paraphrased as 我喜欢唱歌和跳舞. 我喜欢唱歌，还喜欢跳舞. sounds like I like singing and moreover/furthermore I like dancing as well. Or Not only do I like singing, but also I like dancing. as your friend suggested.