1. Yes that is perfectly legal, as there is no international law defining how to use such multi national rivers. The thumb rule is, whoever builds the dam first, gets the right to use the water. Indus Water treaty is the only exception in the world.
2. Of course, dams are build to divert water, that's the purpose. But what we fail to understand is the Brahmaputra in India is mostly rain fed, most of its water it gets, is after it crosses the Indian borders. The Tsangpo is a narrow river, it becomes mighty when it crosses the border and becomes Brahmaputra.
3. Technically its possible, just throw the treaty into the garbage and insist on following internationaly laid down rules.