does a real estate agent have to tell me every offer that comes to their desk?

In the US, they would tell all offers unless you have an agreement that says they won't tell you offers below a certain amount.

Yes. You are paying them and they are working for you so it is in your interests to know of every offer. Why wouldn't you want to know? You're selling a property, don't be insulted. Someone else in a different position (i.e. in dire financial need) might prefer a "disgraceful" offer to no offer at all.

Absolutely YES! All offers have to be disclosed to there client. Some may not however they must. Be sure to do your homework and see what similar homes sell or rent for in your area. Maybe your agents hinting to you to drop the price.

Yes, for you to consider and counter or refuse yourself. I don't see the problem.

That is correct in the UK. What's the problem with that?

the good the bad and the ugly

Nope only ones that she think would be good for you