B.) is wrong. That would be a mix of tenses: "is" and "been erected". D.) is wrong. A bridge can't erect itself. It has to be erected. So it could be "being erected". A.) is kind of correct. But we always say "under construction", not "in construction". C.) is correct.

I agree with Kevin. Both A and C are fine. I would give C 100 points and A 99 points - that is how close I feel they are in terms of acceptability. I personally prefer the expression "under construction." Perhaps that is why I would give C a slight edge over A. Nevertheless, I do not think any native speaker of English would challenge A as a perfectly good answer in this sentence.

@Brian, here noob's a question. The original sentence has 'already', so 'under construction' is odd to me a Japanese native. If I am allowed to ask that why it do not have 'starting' nuance? I'm afraid my making an ambiguous question.

Here is my thought process: For A, “A railway bridge is already in construction” seems fine, but adding “over the river” at the end seems odd. For B, “is” should be replaced by “has.” For D, I would say a flagpole is erecting, but I am not sure if it would sound strange to say a bridge is erecting. That leaves me with C, but the word “already” made me hesitate. I would be happy to accept both A and C as answer, thanks!

A and C both sound fine. Do you need a definite single answer?