Learn English – Is this sentence about fire fighters correct

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.

If you are specifically talking about something in the past, your best bet is option one or three. They're both correct for your usage and they both mean the same thing. The preposition "on" is discretionary - you can use it or not.

In your exact sentence, I recommend omitting "on".

The abandoned building caught fire many years ago.

You do not want to use version two. It sounds a bit odd to me as a native speaker. There are probably cases where it would be acceptable but it doesn't feel natural.

Version four is perfectly fine but not in your example case. The "has" implies that the building is currently in flames and it happened recently... which, since you're talking about something that occurred many years ago, would be incorrect.

Note that it may be helpful to continue your sentence to explain what the end result was.

The abandoned building caught fire many years ago but was rescued by the local fire department.
The abandoned building caught fire many years ago and burned to the ground.