Hello there....Here's a Scripture that got me to meditating about what the mark of the beast really is.
Ezekiel 9:4 "And the Lord said to him, Go through the midst of the city, through the midst of Jerusalem and SET A MARK UPON THE FOREHEADS of the men who sigh and groan over all the abominations that are committed in the midst of it."
It would seem this mark is invisible. This Scripture shows the Lord's angels putting an invisible mark on those who love God and are heartbroken and ache about all the sin around them. They get to have this mark because they are holy and love God's ways. They receive it because of the condition of their pure hearts and minds.
Likewise, the unbelievers and those who are pretending to be followers of God also get a mark (mark of the beast)....on the forehead to show that their minds/thinking is off-course and arrogantly self-centered .....and on their hands because they work to further the cause of Satan.
The other issue you mentioned about the "days being shortened" might be explained with the historical example of Jerusalem being totally sacked in the spring of 67 AD thru September of 70 AD (a 3 1/2 year period). The Romans wanted to DRAG OUT this siege as long as possible so that everyone inside the walls of Jerusalem would experience a terrible starvation. But God did not desire that to happen. He ordered the circumstances to happen more quickly....cutting the time short. Some folks get this Scripture confused and think that a 24 hour day is actually shortened...but not so. It seems to be referring to the actual length of the trauma/trouble being cut short to a smaller amount of time so that His children don't have to endure needless pain.
Another issue you brought up in Genesis 6:4 talks about the "sons of God" living with the "daughters of men." I was curious about that Scripture too and found that the old-time theologians who studied Hebrew and Greek all their lives explained this verse differently than what some think today. They said that the phrase "sons of God" was another name for His true sons/followers and the "daughters of men" was another name for the heathen unbelieving women. God was forever warning His children NOT TO INTERMARRY with the heathen nations. But they didn't listen and continually disobeyed marrying ungodly people. Verse 5 shows how wicked everyone had become thru ungodly marriages....only 8 souls were righteous enough to make it onto the Ark that Noah and his boys built. We are told that when we get to Heaven we will not be marrying but will have new bodies much like the angels. This seems to indicate that angels cannot marry/breed because they are spirit beings and not physically able to produce physical children.
Just a few thoughts.
THE BOOK is our plumbline so we don't get off track...and digging around in the Hebrew and Greek a little doesn't hurt any either. Blessings on you as you study the Scriptures and ask the Holy Spirit for new insights. It's lots of fun but also very necessary.