Learn English – If “discuss about” is redundant, what about “discuss with you about”

"Over" in this context means that you will be talking or taking some similar action during the time when you are eating or drinking something, or (much more rarely) doing some other activity.

If you used "with" in this case it would change the meaning. Consider these sentences.

Bob and Willard fell in love over dinner

means that they fell in love while they were eating their dinner. If you say:

Bob and Willard fell in love with dinner

it means they really, really like their dinner. Using this construction, even where it is less ambiguous, to mean "while eating dinner" is not very idiomatic. You can have wine with dinner; you have a discussion over dinner or during dinner.

You can restate this in other ways, however.

Let's work out the details over a couple of beers

can be restated as:

Let's work out the details while we drink a couple of beers

but this sounds a bit awkward and stilted. My guess is that that's why the shorter "over" idiom came to be--it avoids the ambiguity of "with" but is simpler than constructions like "while we eat" or "to accompany" or suchlike.

As a mnemonic--and a plausible origin--think of two people sitting at a table drinking tea. The tea is in cups on the table; the discussion passes over it, above the table. The discussion is literally happening "over" the tea.

1) Sentence 1 is OK, but you can simplify it:

This is nothing to worry about.

This holds the meaning of thing (or whatever the subject is) so there is no reason to repeat it, unless it needs specific emphasis.

2) Yes.

3) The phrase I mentioned above solves the problem of whether to say a thing or the thing (your comment in 3) in your question, whether to use "a" or "the").

But if you want to use "a or "the" as in your example, I would stick with "a" unless you need to emphasize a particular "thing". It is unlikely to be "the" only "thing", as we all have plenty to worry about.

An example using emphasis might be:

You have been late to work a lot recently. Your attendance is the thing you need to worry about.