Your citing of Genesis 6:6 and Ephesians 4:30 is good. That's probably as far as we can go in answering your question, however.
I want to say God was indeed grieved by the sin of His chief angel, Lucifer. God had invested a great deal in Lucifer. Lucifer was beautiful to behold, and he perhaps had a special place, or ranking, in the third heaven. Perhaps he was an angel of angels, a leader of other angels in the worship and service of God. To say God had no feelings whatsoever when He found sin in Lucifer and was forced to eject him from the third heaven, seems wrong. As to what those feelings were, however, I think the Scripture is largely silent.
In re-reading the book of Job recently, I noticed something interesting, and I'll pass it along to you. We read in 1:6 and 2:1,
"Now there was a day when the sons of God came to present themselves before the LORD, and Satan also came among them."
"Again there was a day when the sons of God came to present themselves before the LORD, and Satan also came among them to present himself before the LORD."
The thought came to me: Hmm, the sons of God presented themselves before the LORD. I wonder if this event is repeated on a regular basis throughout history.
I suggest--I repeat, suggest--that this formal reporting, as it were, may in fact be a regular occurrence in God's universe, at least in the spiritual realm.
My thinking on this is as follows: 1) God alone is Sovereign, and He is sovereign over everything and everybody in all creation; 2) He holds things together (all things cohere through Him and the word of His power); and 3) no one can escape accountability to Him.
"And there is no creature hidden from His sight, but all things are open and laid bare to the eyes of Him with whom we have to do" (Hebrews 4:13 NAS).
If these things are so, then perhaps God has a "standing appointment" with the sons of God (i.e., the fallen angels) to "keep tabs on them," so to speak. Being omniscient, He knows what they've been doing, of course, but the verses in Job simplify things for the benefit of us readers. Since His fallen angels are not omniscient (nor are they omnipotent or omnipresent), they need to be reminded frequently of what they may and may not do.
In particular, I think God, in His watchful care over His children, allows the infernal hosts of wickedness to "sift us as wheat" from time to time, as He did with Job and Peter, for example.
Job: "Then the LORD said to Satan, 'Behold, all that he has is in your power; only do not put forth your hand on him.' So Satan departed from the presence of the LORD" (1:12).
Job: "So the LORD said to Satan, 'Behold, he is in your power, only spare his life'" (2:6).
Peter: "'And the Lord said, 'Simon, Simon, behold, Satan hath desired to have you, that he may sift you as wheat: But I have prayed for thee, that thy faith fail not: and when thou art converted, strengthen thy brethren" (Luke 22:31-32).
God, however, puts limits on what they (and the devil) can do, as He did with Job, when He told Satan he was not allowed to take Job's life (2:6). God also knows if and when we will repent, if in our being "sifted" we fail the test, as with Peter:
"'But I have prayed for you, that your faith may not fail; and you, when once you have turned again, strengthen your brothers'" (ibid.).
In conclusion, obviously God and Satan are on speaking terms, and Satan is on a short leash, as it were. Satan, however, knows that his time is short. His authority and activity as the "prince of the power of the air" are finite and will end one day when he is cast into hell, which was designed by God for the devil and his angels. Sad to say, many others will likewise be cast into hell one day, and I'm sure this, too, grieves God.
Consequently, God is patient and forbearing with us. Moreover,
"The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish , but that all should come to repentance" (2 Peter 3:9 KJV).
I believe Satan can never, will never, repent. Human beings, however, God encourages to repent, and they are free to do so until the day they die. Once they die, however, repentance is not possible.
". . . as it is appointed unto men once to die, but after this the judgment: So Christ was once offered to bear the sins of many; and unto them that look for him shall he appear the second time without sin unto salvation" (Hebrews 9:27-28 KJV, my emphasis).