Nice points raised by Swapnil. It is my pleasure that someone think on my story so deeply. The Explanations are.
1.To understand mathematical concept of dimensions. To predict aliens of other dimensions and to raise some theories regarding dreams. Yes, it does not raise any global problem or teach moral values.
2. Of course dimension is a fundamental concept of vector mathematics and physics.
(a) Picture was not alive. She saw everything in dreams. Everything in unconscious mind.
(b) There is no point of time contraction in the story.
(c) Love of first sight. Of course the aliens of other dimensions have so much power that they can contact with our dimensions. But not physically. This is why he came only in dreams of girl.
3. Not physically. But through the other ways like telepathy, dreams etc, he contacted to the girl.
4. That is the case of his boy friend. There are many cases in history where a couple found a baby, though their medical report comes out to be negative. Here I introduced a thought that such cases may be the result of combination of a person with some alien.
5. As already mentioned in the story they have no definite shape, but can take any shape like a shade due to their low dimensions. Their purpose of taking shape was to look them by the girl. Otherwise there was no need to take a shape. Here I also kept in mind the younger reader level of Vigyan Pragati.
6. Story must have some interesting fantasy for younger people.
7. Already explained
8. Already explained
And after all this is not a research paper, just a story which must have room for imaginations beyond the facts.