Is "brain training" effective?
I believe the hype about brain training got started with Susanne Jaeggi's paper  on n-back training and its alleged improvements to fluid intelligence (Gf) and working memory (WM): 

The experimental design was called into question by papers that followed and tried to replicate similar results. Most of them could not detect a maintained improvement in WM and Gf. Further, most studies did not find it to generalize to other skill domains.

I'm not sure how to interpret the third question.

Numerous studies have shown that mental stimulation is effective in reducing the risk of Alzheimer's disease. The more interesting question is probably whether brain training can ameliorate attention deficit...