Are the following sentences natural to a native ear? Not in NA. You're mixing your metaphors.
1. Believe me, I am not trying to take a shot at the issue; I have accepted it as a fait accompli. We don't 'take a shot at the issue', we 'take a shot' at a solution (try to fix it) or we 'take a shot' at someone (insult them or otherwise try to cause psychological injury).
2. I am sorry, I think you
mighthave reached the wrong number.
herhaving her around will hopefully take some load off my plate. (I was talking about a new colleague). We don't have a load 'on our plate'. We might say, "...take a load off my back." or "...take some things off my plate." or "...take some of the load off me."