Hi Hela,
My French, I'm sorry to say, is not good enough to verify the precision of the translations (though I was happy that I was able to understand the general meaning in all of them), so I'm going to comment only on the naturalness of the English.
4) Normally or Usually (either is okay), the police - use this, because it's gender-neutral do not carry firearms. Weapons is very broad - the "night stick" that many police carry is still a weapon of sorts.
6) You can use either arrested or have arrested. Police takes the plural verb though, so it's have arrested, not has arrested.
9) Now I'm going to look igorant, but is it closer to say "I would really like it if you would help me..."? There's no difference in repair / mend / fix in this context. You can use "can't manage" but say "can't manage it" or use the other version you suggest.
10) Again, I may be quite wrong, but is it "She left on her holiday/vacation a few weeks ago" rather than "She's been on holiday..."?