Now I can answer your questions
At a military level it means to fight. The traditional view and one adopted by all the legal schools is it means defence of Muslim lands.
The very notion of "Muslim lands" ridicules the notion of defensive jihad, because it allows for an offensive strike, say if a portion of the people in the land turn away from islam. War is then acceptable to carry out because they are defending muslim lands.
It means defence of traditional Muslim lands to protect from invaders. Afghanistan (1980s) was a traditional defensive jihad, attacks on other lands a la Al Qaeda and ISIS are offensive jihad.
It's also worth noting that islam only spread by warfare, mohammad gained very few followers from preaching, he only gained power through allying with caravan raiders and jihad of the sword.
You should read the Oxford handbook of theology,it is a history of the development of Islamic thought, it's a history book as much as anything, Islam also spread peacefully, places like Ethiopia and Indonesia weren't conquered violently they spread via trade,Sufism played a large role in the expansion of islam. Though it's untrue to say Sufis never fought but it's also true that the early post Mohamed era was expansionist and certainly on the peripheries there was lots of fighting to conquer areas, but those were military decisions and that was then and this is now. Maududis islamism is a totalitarian, expansionist ideology. Good luck with that, they never actually achieve their goal.
When it comes to deriving religious rulings, purist salafis who like sufis tend to be political quietists orient towards the Meccan period of their prophets life and believe that their role in the current era is to proselytize and bring others to the faith.
Whats your understanding of Abrogation? The strong verses override the weak (early) verses and you see this in Mohammads life, when Medina-stage mohammad overrides Meccan-stage mohammad. The problem, and I've covered this before, is that the scholars preferring Meccan-stage Mohammad's teaching are too small a group to make a difference, as much as I prefer they weren't.
That's the position of all the legal schools in existence.
Sure about that?
Abrogation Defined:
"The law was laid down in the period of [Mohammad] gradually and in stages. The aim was to bring a society steeped in immorality to observe the highest standards of morality. This could not be done abruptly. It was done in stages, and doing so necessitated repeal and abrogation of cetain laws."
Imran Ahsan Khan Nyazee
Islamic Jurisprudence
Abrogration is informal and therefore mileage may vary on the particular school of thought. I guess the point is understanding how Muslims derive opinion via the Quran, the hadiths and further secondary sources. There seems to be a populist view that later verses always abrograte earlier verses but it's not one I hear from Muslims, but this isn't a subject I'm so familiar with if I'm honest and I have to pass on it.
Note that mohammad only got more violent as time went on, not less violent.
The Quran comes in two parts in the first part he was able to proselytize and educate until he was expelled from Mecca, in the second period he fought those who expelled him and conquered Mecca. Most Muslims, certainly purist salafis believe the current period represents the first era and are oriented towards those verses, the jihadis otherwise
Most of the violence in Sunni Islam you see today derives from Maududi and Qutb's islamism and the supposed need to form an islamic state that they made up.
ISIS claim that the number one reason for why they hate is that others are unbelievers. This is consistent with the Quran verse "fight until all religion/belief is for Allah". If all belief is for Allah then that necessitates no other states except an islamic state or caliphate.
Their number one goal is establishing gods rule on earth (hakkimiyya) and replacing illegitimate (taghut) regimes in Muslim lands with an authentic caliphate where they rule according to their own interpretation of god's law, which as we know is brutal as fuck and should in my opinion be resisted militarily with far greater brutality. There is a religious dimension to their caliphate of course but these groups are politically islamist.
Where does this leave other Muslims?
Unless they are islamist they are cool, Islam itself doesn't support suicide or killing of innocents, even if they are islamist they may not propose violence as a solution,they may just feel that a caliphate is the best solution for the Muslims.
Jihadis and militant islamists are a real threat because they are willing to die for their political goal. They seem to attract street thugs, petty criminals and small time gangsters who are attracted to their salvation theory and who see them as a much bigger gang. These people typically don't know very much about Islam which enables jihadists to sell their twisted violent politicised form of Islam to people who are probably already disenfranchised with their life and who likely feel alienated by society, and who feel a sense of injustice is being meted out to Muslims who see the west going to war in Muslim lands and who are religious and want to get back into the fold but because of their behaviour don't know how to redeem their souls. If we don't want to contribute we must try to stop alienating innocent Muslims because it's an injustice to blame innocent people for crimes they haven't committed and that creates a cognitive opening for terrorists to sell their ideology.
https://www.academia.edu/12629134/Its_A_Trap_Provoking_an_Overreaction_is_Terrorism_101