lol the first quote there is in reference to fighting against people who usurp and take over your lands. It also includes a part saying Allah forgives if they desist. So in other words, it outlines fighting back if people take your lands or persecute you. In fact the previous verse explicitly states not to transgress i.e. to not exceed the enemy in violence, it's very eye for an eye.
The second quote is taken completely out of context of the surrounding quotes in the Qur'an, a mere 5 verses before establishes this context "Do they await but that Allah should come to them in covers of clouds and the angels [as well] and the matter is [then] decided? And to Allah [all] matters are returned." It's telling Muslims that merely praying to Allah won't help them, they have to put in their own effort too. Fighting is then used as an example in the quoted verse to highlight that although it might be abhorrent for you, sometimes it is necessary to fight back and you cannot just be reliant on Allah doing everything for you.
At this point I would like to draw attention to is that the Arabic language is very different from ours. Jihad doesn't actually mean war. In the Arabic of the time, jihad was a broad term for struggle. Terms in English such as "debate", "strive", "protest" etc. would all come under this umbrella term in Arabic. So verses talking about jihad are not necessarily referring to war, simple to "strive" or "struggle", which can be something as peaceful as debate or discussion. In fact Arabic speaking people would refer to Gandhi's movement in India as a "jihad" despite it's non-violent nature. As such the next few quotes on that page by no means explicitly incite violence at all.
As for 4:89, whilst it may seem violent at first, reading the next verse, it states "So if they remove themselves from you and do not fight you and offer you peace, then Allah has not made for you a cause [for fighting] against them." So it is literally referring to attacking people who attack you first, a concept that isn't really unjust.
In fact verse 5:33 refers to violent punishment it is preceded by a verse that states "that whoever kills a soul unless for a soul or for corruption [done] in the land - it is as if he had slain mankind entirely. And whoever saves one - it is as if he had saved mankind entirely." Islam is strongly built upon "eye for an eye" justice, and as that earlier verse i posted a few paragraphs back makes evident, transgressions beyond an equal punishment are regarded as sinful. "Allah forbids you not, with regard to those who fight you not for (your) Faith nor drive you out of your homes, from dealing kindly and justly with them: for Allah loves those who are just." is in fact a verse that promotes mercy.
Verse 8:12 is actually taken completely out of context. The entire translation of it makes evident Allah is talking to angels and not Muslims lol.
The rest of the verses either automatically assume jihad means holy war, when it doesn't necessarily or refer to Allah punishing disbelievers in hell, not Muslims themselves committing violent acts.
