Sorry for the delay
1) I can explain everything if you'll just give me a chance/an opportunity.
If you give me a chance/an opportunity to speak, I'll explain.
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The answers you gave here were that only 'chance' is correct. Why does 'opportunity' not work here in the two sentences?
It's idomatic. Opportunity sounds like a you need the time or the place, while "give me a chance" is more of a mental thing - you'll hear what I have to say with an open mind, or watch what I do prepared to believe I did it well, without pre-judging me.
2) I never get/have a chance/an opportunity to relax these days.
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Your said "get a chance" is my preference, but "opportunity" doesn't sound weird.
Do you mean we can use 'get a chance' or 'have a chance' or 'get an opportunity' or 'have an opportunity' here?
This sounds natural to me. I don't have many opportunities to; I don't get many chances to; I don't get many opportunities to.
3) I'd like to take/seize this opportunity to thank you for all your hard work.
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What is the difference in meaning between 'take this opportunity' and 'seize this opportunity' here?
Seize is more agressive. Someone can give you an opportunity and you can then take it, but if you seize it, you may interrupt.
4) Denise never misses the chance/opportunity of a free meal.
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Your answer: Neither. Maybe "the opportunity to accept a ..."?
I got the example 'Denise never misses the chance of a free meal' from online dictionary. I don't know why 'chance' is not fine here? Do you think chance really doesn't work here?
It just sounds really odd to me. Like, if she shows up, maybe there's a free meal, or maybe there's not, and she'll take that chance. But don't worry about it. It's probably just personal to my ear and doesn't sound odd to anyone else.
5) If I had a chance/an opportunity to become a university studednt, I would study as hard as possible.
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Does 'had an opportunity' here mean 'it's likely to happen' ?
Not necessarily. It the situation is possible, that's all. It doesn't say how likely it is that the situation will arise.
6) You should take the chance (=use the opportunity) to travel while you're still young.
Can I use 'opportunity' instead of 'chance' here as in ...take the opportunity to travel... ?
Do the both mean the same?
I'd say so.