Again Hades wanted to audition the Winter Knight as a possible mortal custodian of the artefacts, so a link was made both by circumstance and design, Harry had to break in to maintain the integrity of the link, an invite would undermine it.
Mab isn’t an Intellectus, so she does not have a comprehensive knowledge of the ways. There are realms in the NeverNever shut to her, those of more powerful gods content to dwell in their own domains like Hades, some friendly, some not, and it depends upon what information they deign to give her.
Remember Mab’s power level through her mantel appears to have been deliberately set so that she is as powerful as she can be to be able to manifest almost full time in the mortal world without breaking reality too much, (except for the weather) even the addition of the Summer Knights power via the Stone Table to her Mantle is enough to cause an ice age. Her power level is too low for a general intellectus, like the Mothers or Uriel.