To distinquish "train or teach" is improper. I am new to aikido but know some fundamentals -from reading this and other site material, books and heart-felt intuition. It is very clear to me that teaching and learning/training are yin-yang, and can not be seperated.
In theory, yes.
In practice, with only so many hours in the day and so many hours in the week, it's not uncommon for an instructor to spend less and less time training. This isn't unique to aikido or martial arts in general. This happens in many, many activities.