Dealing with anxiety about answering questions during presentations
There are other questions about "imposter syndrome" on this Stack, it might be useful to look through them because some of what you describe might fit into that area.
Besides that, I think the best way to feel better about answering questions during presentations is to do it a lot. Seek out opportunities to present to a "friendly audience", and ask that they challenge you with questions. Talk about your research informally with fellow students in your area. Do all of this in English, in case you typically use another language in those contexts.
You can also try to plan ahead for certain questions or areas of questions, and even make slides to respond to those questions ahead of time if they are asked. Generally I wouldn't suggest purposefully leaving information out to prompt certain questions, but it is rare that you can fit every single caveat and counterexample and piece of background into a talk.
If you can't figure out what question someone is asking, try to ask it back to them, even if you are off the mark or don't get it exactly right - that's usually more productive than just asking someone to repeat. I see native English speakers including everyone from students to full professors have trouble understanding what someone is asking about all the time - it's quite normal. Also, questions asked during a talk aren't like exam questions where a grader is judging your answer based on some rubric for that specific question. Usually the asker is hoping to get you to elaborate on something, so even if all you can pick up is a key word you can repeat back a possible question based on that key word, or just start elaborating on that area. I'm also a fan of being honest with language difficulties. I would never think less of someone who just gave an entire talk in their non-native language but doesn't understand a particular word or phrase I used.
Lastly, I don't think academia is nearly as "judging" as you may think it is. Especially when you are presenting your own work, know that you are the best expert in the world in your own work. PhD-level research does build on what has been done before, but ultimately if it's research worth doing as a PhD student it is pushing some boundary of knowledge. You're the only person who has yet crossed that particular boundary, and the whole point of giving an academic presentation is to bring your colleagues up to speed.
Your problem starts with how you approach giving the talk. You say:
I have a script for my talk, rehearse it so many times to the point I almost memorize it. I even practice my facial expressions and voice tone during the talk. I just learn and practice how to present my "ideal" academic self to colleagues.
Given you are presenting in a non-native language, this is understandable, but you should try to be more spontaneous in your talk. Start by reducing your verbatim script into shorthand, and remove the phrases/expressions that you find easiest. Once you have become comfortable with that, reduce your script further so that it occupies just one sheet of paper, on which you outline the structure, key points, and any quotations.
Once you have become more spontaneous in how you give a talk, you should find yourself better equipped to handle questions on the spot. As for dealing with these questions, remember that conferences are about presenting "work in progress" and providing an opportunity to discuss such work with peers at a formative stage. In that context, you should expect to be challenged.
Think of the tough questions as feedback, and engage with it in good faith -- that is to say, try to respond with some discussion relating the ideas/issues raised by the question to your work, even if you cannot actually answer the question. Think of it as a very brief seminar discussion or supervision, and participate in that spirit:
- do not dodge the question;
- do not change the question to something you wish the person had asked; and
- "I do not know" is perfectly acceptable as a starting-point for an answer, as long as you then elaborate by making a connection to something you do know (practice saying expressions such as
- "I do not know about this issue specifically, but what I can say is that..."
- "I am not sure about ..., but it may be connected to what we have observed with ..."
- "I have not got enough information/evidence to be sure about this, although I suspect that..."
When someone asks you a question, pause before you answer. This gives you a chance to gather your thoughts and make sure you're answering the question they asked (and not the question you assumed they were asking when you heard the first few words from them). The pause will also reassure the asker that you've really listened to them. I often find that during such a pause, I come up with a better, more coherent, answer than I would have otherwise. Pause for what feels to you like an awkwardly long time (it will feel much shorter to the audience). One way to force yourself to pause is to breathe in slowly.
Remember that the audience is on your side; they want you to do well. There might be someone in the audience who likes to take people down, but other people will recognise this as mean-spiritedness; they will have empathy for you. And it won't be your job to deal with such a person (beyond a good faith attempt to answer the question). The conference or session chair will step in if things get out of hand.
If someone asks why you didn't do Y instead of X, treat it as a suggestion rather than a criticism. It's usually fine to say something like "for this experiment, we did X because it was convenient/familiar/etc., but it would be interesting to repeat the experiment with Y in future".