The Parma Magica is not affected by the Aegis of the Hearth. This is for gameplay reasons as the Parma and Aegis are two elements needed for the setting to function. If you want to rationalise it in universe a good explanation is that the Aegis was building on the work of Bonisagus with the Parma Magica (by his apprentice Notatus) and so they interact in a positive way. you can put your Parma up in an Aegis of any strength, no problem.
How the Aegis interacts with supernatural abilities is a bit more of a gray area. A common interpretation is that all supernatural abilities are impeded by the Aegis just like spellcasting and might based powers are. This could either be a penalty of (3+Aegis Magnitude) or the full penalty of (Aegis Level/2) depending on your interpretation. Second Sight may be a rare exception to this as it ignores the targets magic resistance entirely, but it might not be as the Aegis prevents Intelligo effects that would otherwise ignore magic resistance.
It's also worth saying that the Aegis only makes it harder to use spells/powers, it only 'blocks' them completely if the roll is penalised so much it fails or can't produce the effect. That might be what you mean by blocked, but I thought it was worth saying just in case you had misread how the Aegis works generally.
This thread has a very good breakdown of the Aegis, though some things are still up for interpretation: