No they were not. They gave each other permission, they were invited. It was not an invasion. The whole word invade becomes meaningless if every entering is an invasion and a lot of obviously legal things become impossible like the gatekeeper healing people in turncoat.

Yes, but remember when Harry would have died from his first encounter with the Corpsetaker but for Gard's intervention?  The reason he almost died was because of lack of proper training against mental attacks..  The reason for his lack of training weren't the usual ones, i.e. Harry's own laziness or lack of exposure to it because of Justin, but because the Council feared and prohibited any form of this magical training beyond the minimal defensive type.   So the Council prohibited it even if permission from the two parties was granted..   To their credit Harry and Molly both thought this was stupid and trained each other, however they did it in secret because it would have gotten them into a lot of trouble...  Enemies on the Council may even have gone so far as to declare it an infraction of the Law.

This struck me as not quite right, so I looked it up.  It's an interesting point.  She kills no one.  She simply presents an opportunity for people to see what they fear they might see.  The victims killed each other.

It's a little spooky ethically speaking.  Think going into a grocery store and handing the cashier typing paper that is made to look like money.  Immoral, but no laws broken.

However her first victims, her friends that she thought she was helping were seriously harmed by her entering their minds and trying to change their perception of things..  Yeah, the Law was broken, one isn't allowed to enter the mind of another... It is so strict that most members of the White Council have only the merest and ineffective defenses against an attack on their minds, they fear it that much... Molly and Harry were in violation to some degree by practicing on each other.

In Turn Coat, checking Luccio for corruption was definitely against the Law (as enforced by the Council, whether or not it would be corrupting). I think it was still justifiable, though.

  Agreed, however for someone already under the Doom, I seriously doubt the Senior Council would give her another bite of the apple...  What Harry's point was that it is very dangerous for Molly to decide when it is or isn't justified to break the Law..  Remember that is what got her into trouble in the first place, not breaking a law she didn't know existed but thinking she could go into her friend's mind without thinking through the consequences... She hadn't learned her lesson is what he was saying.

From Turncoat:

And it goes on and on. The laws of magic have nothing to do with morality as explained by Captain Luccio.

And Margaret was right, without justice there is no point.  Common thugs can give a neighborhood protection, but who wants to live under the rule of thugs?   Morgan's long harassment of Harry was about enforcing the Law, in the end as he died he realized it is also about justice and morality and he was wrong.

The thing to remember about the laws of magic have nothing to do with morality, and everything to do with protecting humanity from Warlocks, Outsiders, and those who would interfere with the flow of time.

 But it is about morality, it is ALL about morality, it is the basis of law..  A lot about black magic is it is a short cut to getting things done, because there are no rules..  You sneak a love potion in, innocent, just want to lower inhibitions... No harm, no foul... Really?  Not about morality, it is about protecting humanity from warlocks etc....  Well, consider, the young apprentice who has gotten far enough in his or her studies to make one and use it on someone he or she doesn't care to woo or who won't give them the time of day... Short cut to an end...  Harmless?  Think again the young wizard gets by with it, no thought of the repercussions for the object... Or the repercussions for the young apprentice who is now tainted by it, may become a bit lazy take more short cuts oh, now we have a warlock on our hands.. Or take Victor, some talent, got a hold of some books, perhaps the wrong books, but his original motives were not evil...  But then he found the short cuts, they got out of hand, suddenly he is a very dangerous sorcerer and people are getting their hearts torn out by remote control...   

In the RPG, Billy asks exactly this. Harry's answer is that it's not technically altering the person's mind or body -- it just lowers inhibitions by a lot, not much different from getting a girl liquored up.

So it's not a violation of the laws of magic, but it's sleazy as hell and not really a good thing to do either.

Taking advantage of anyone liquored up can be seen as rape..  Liquor, drugs, love potions affect one's judgement, thus one's free will to make choices..   So yeah, it is a violation in my book.

Sure it is but Harry's interpretation is pretty stern and he was trying to keep Molly safe. Molly did something similar when she looked at Harry in small favor and Luccio, who is sometimes somewhat more relaxed, did not say a thing. This is again a gray area.

No, not a gray area, whatever her motive, she broke the Law... 

Turn Coat page256

"You broke the Laws of Magic, Molly.  Willfully.  Even though you knew it could cost you your life.  Even though you knew that it could also cost mine. 

Not a gray area at all, it could have cost them both their heads... Highlighted by Morgan's dying words to Harry about Molly...

page 394 Turn Coat

"I didn't tell them about Molly.  What she tried to do to Ana.  I. . . I didn't tell.

A couple of things going on, he is telling Harry in his own way that he was sorry for being such a hard ass with him.  He is telling him that he has hope that it will work out for Molly, that basically she is a good person..  However it doesn't change the fact that if he had turned her in, she would have lost her head, and along with it Harry would have lost his head.  She did break the Law of Magic,  and would have paid the price if Morgan had turned her in.

No comparison is 100% correct because then things would be identical but it is about how a comparison can help us. Some people can cure themselves and that is exactly what Sanya started when he threw away the coin.

He was helped by the insight he got when he heard the other denarians talk about him. A beginning warlock might get insights in other ways. Part of the problem is that young wizards have little or no knowledge about the dangers.

Except that isn't how the blackstaff works,  there is only one, and the wielder is assigned the office to wield it...  Yes, free will to accept the office, also the blackstaff isn't constantly in Eb's head, unlike the Fallen of the Coins..  True, young wizards have little knowledge when their talents awake without guidance from a mentor, but again this has nothing to do with the blackstaff...  If it were so simple that a young would be warlock could be so easily cured, why isn't Eb busily waving it at would be warlocks instead of them getting their heads lopped off?

Of course you can cure a warlock just as you cure a denarian. At the end it is just a matter of free will however difficult.

But at the end it is not very likely most of the time so the wardens just assume that it is not possible or too dangerous and as a working hypothesis it works even if they kill a few curable warlocks.

The knights always try to cure the denarians even when that is dangerous but they are more idealistic and maybe less practical than the white council.

I believe the Merlin explained it, that once past a certain point, the cure rate is next to zero...  Harry was caught in time, though he has struggled with using the black and has been called a warlock even now...  Molly, I fear would in the end have lost her head because she had a bad habit of slipping back into messing with other people's brains..  So Mab did both her and Harry a favor preparing her to become Winter Lady, it saved her.   Waving the black staff at a warlock isn't an instant cure or a cure at all..