Learn to be a politician and avoid an answer while providing unlimited volume of words. Then you may run for office.

I struggle with this while I am put on the spot. Getting a bit nervous seriously throws me off my thinking game. I tend to come up with the best responses a few minutes too late. Sorry, I don't have any tips for you but just wanted to comment and commiserate.

"Any suggestions as to how to improvise in real-time when you don't have the slightest clue about what is being asked from you?"

yes. find out what is being asked of you. you can do this by speaking. ASK!

if you are making a speech and not expecting an answer, make the question part of the speech.

for example:

"when you ask me to speak about 'people's relationship with their parents' are you speaking about young children or adult offspring? if you mean children, then bla bla bla bla. [you can drill down from there too if there are two paths.] on the other hand, if you mean adult offspring, bla bla bla [and likewise you can drill down]."

if you're stuck because you have not thought about that topic before, make the confession of that part of your speech.

"i confess i have not given this topic a lot of thought. i wonder what i would do if...."

adapt!

g

One of the most common and unfortunate problems people have while speaking, particularly in front of others/audiences, is talking too fast. Another is the insertion of filler words and noises. It takes considerable practice to get both of these under control, but once you do, your thinking will keep pace with your mouth.

From what I have read so far, you have no other problem than not being able to come up with a rapid response, which happens in any language. I have a drawn out "Weeelllll...." that I use a lot and in French " Dis donc...;" is used all the time. it means "So, well, ummm....." and then you get on to it.
That IS a natural speech pattern. May be we need to give you some phrases ?

Wait! Does this explain Cheeto? No, he can do neither properly....carry on!

If it was easy it would not be part of the exam, but remember you think best when you are relaxed. So the important things are to have a few fillers memorized, that may have little to do with any of the questions you may be asked, things like asking for repeats or just saying honest things like "I find speaking the hardest," which you can drop in when needed, the point being that you will not use them in all probability but just knowing they are there will help you to relax.

I think and speak at the same time.

If someone asks me a question that I don't know how to answer right away, I'll ask them to repeat themselves. I'll be thinking of my answer while I ask them to repeat themselves and while they're repeating their question.

I mainly do this to give myself time to gather my words correctly so they are understood and my point comes across clearly.