Hello. I will be very grateful for some help.

1)Do you think it's possible to use "announce" in the following pattern: "he announced to reporters that..."?
2)Do you think it's natural to use "in answer to" in the context: "authorities have taken these measures in answer to the recent acts of terrorism"?
3)Is it possible to say "to decare a decision" or is it "to announce a decision"?
4)Is it natural to use "recognize" in the context "to recognize defeat"?
5)Is it natural to combine "general" and "national" in one word-group: "general national (nationwide) elections"?
6)Which article would you use in the context: "he announced a/the(?) decision not to participate in the elections"?
Thank you very, very much for all your help.

1)Do you think it's possible to use "announce" in the following pattern: "he announced to reporters that..."?

You would use that only if the announcement were taking place in a public press conference.

2)Do you think it's natural to use "in answer to" in the context: "authorities have taken these measures in answer to the recent acts of terrorism"?
Yes, it's fine.

3)Is it possible to say "to decare a decision" or is it "to announce a decision"?
"announce" is usually better.

4)Is it natural to use "recognize" in the context "to recognize defeat"?
I'd need to see a complete sentence to be sure.

5)Is it natural to combine "general" and "national" in one word-group: "general national (nationwide) elections"?
Yes, it's fine; it's basically stating that the election is not a special election for only one or two purposes, but is an election for a variety of offices, for example, that come up for reelection regularly.

6)Which article would you use in the context: "he announced a/the(?) decision not to participate in the elections"?
If there's only one decision to be made, then either one will work.