Correct. As a rule of thumb (assumed 50% hit chance) the +1 is actually a +10% difference.
No, it's almost never a 5% change in probability. It's always a 5 percentage points change, but there's a huge difference between percents and percentage points
Depends on your attack bonus. If you have a +31 to attack an extra +1 would increase your change to hit by 33%, that's a lot.
The actual AC is unimportant. Whether or not the +1 happen to coincide with 5% depends on the difference between your attack bonus and the opponent's AC.
With the D&D system it's actually impossibe for the 5 percentage points increase to ever be a 5 percent increase.
You would get that if you hit on 2-20 without the increase and on 1-20 with the increase. As you can never hit on a 1 it can't happen in D&D.
The closes the 5 percentage point increase gets to also being a 5 percent increase is if you hit on 3-20 without the increase and on 2-20 with the increase. In this case the 5 percentage points increase is also a 5.8 percernt increase. That's the closest to them being equal you can get in D&D
PS: To make the 5 percentage points truly equal 5.0 percent you would need to hit on 1 to 20 without the increase and on -1 to 20 after the increase. Something you can't get on a D20 anyway.