So, during the whole seven year gap between the time Suzaku murders his father and when he reappears again as a Britannian soldier, there isn't much information there. Which seems strange, since that would be a rather interesting period to explore. Especially since they never bother to explain thoroughly how Suzaku ended up with the ideals he initially has. So below is just a bunch of shit I made up (pulled from an old app I wrote and edited some) to fill in that gap and flesh things out, that's mainly based on conjecture, and what little bit of canon dialogue is given away about it during the series.
Suzaku's father, Genbu Kururugi, was the last Prime Minister of Japan. When Suzaku was only 10 years old, the nation of Britannia invaded, and Genbu wanted his forces to fight to the last man. Suzaku thought that was insane, and feared the Britannians would crush them, killing countless people in the process. He argued this with his father, and in a desperate, angry moment, he ended up killing Genbu. Suzaku's crime was covered up by his father's political allies, and the public was told that Genbu committed suicide, rather than send his forces to be slaughtered by Britannia, the way the rest of his Cabinet had wished, while Suzaku was placed into hiding. The government was thrown into chaos by Genbu's death, and less than a month later Japan surrendered unconditionally to the conquering Britannians, and was renamed Area 11.
Its not actually known what happened to Suzaku during his time in hiding. But, it is known that Suzaku's chief combat instructor, Tohdoh, was part of the resistance group, the Japanese Liberation Front. It's also known that other members of Suzaku's family funded the resistance movement, but were captured and executed, leaving only Suzaku and his cousin Kaguya as the last surviving members. So, purely as headcanon, Suzaku was taken in by the JLF initially and kept under their protection. In his early days, he would've been kept away from anything too sensitive, but gradually pulled into the group, even joining in on a handful of missions, as he started to grow and his obvious physical talents began to really catch people's attention.
During his time there, though, he saw the resistance movement grow and the conflict between them and the Britannian forces escalate. He saw how the JLF would use increasingly aggressive and underhanded tactics, descending into outright terrorism, and he saw how the Britannians would respond by making the Japanese (now referred to as "elevens") suffer. He watched as innocent people got caught in the crossfire, as his relatives were captured and executed, while he-- the boy who murdered his father-- was protected. He finally snapped when, while wandering around the ghettos one evening, he heard people wondering where was the peace that Genbu died for.
By then, Suzaku had deluded himself into believing that his father had died for the sake of peace. Sure, he knew it was a lie, but he buried the memory of his father's murder deep within his mind and believed in the lie so much that he decided that he would make it into the truth, and he would bring about the peace his father 'wanted'. It was then that he grew to reject armed resistance and terrorism as a justifiable means to an end, and walked out on the JLF. He still fully understood fully why the JLF was doing what they did (its not as if he enjoyed being conquered by Britannia any more than than they did), a free and peaceful Japan had to be earned the right way. Even if the JLF won, they'd have to face the people, many of whom would be asking why they so coldly and ruthlessly sacrificed their loved ones to their cause. He also rejected his family's inheritance, leaving it all to Kaguya. His public reason for that was that he didn't want anything to do with blood money, but privately, he was wracked with guilt and didn't feel that he deserved anything from his family. He also wanted Kaguya to have the resources to live a good, peaceful life in the Chinese Federation.
He resurfaced years later, having become an honorary Britannian, and joined the Britannian military. He believed that if he worked his way into their system, then worked his way to the top, he'd have the power to change things for the better. His plan was that, if he could stop the resistance, he could achieve two important objectives. The first being that there would be a significant reduction in violence, making Japan safer for everyone. Secondly, he'd earn the trust of the Britannians, and he could leverage that trust to not only get them to stop cracking down on the elevens, but to elevate them and make Japan a prosperous nation once again, forging a true peace between Japan and Britannia.
I think all of that goes a long way towards explaining some aspects of his early relationship with Kallen, since he really seems to understand why she's part of the Black Knights, and never seems to hold any real animosity or malice towards her, even though she openly despises him. He sees a lot of himself reflected in her, which could be why, when he first finds out, he pleads with her to leave them. Not only that, but rather than rat her out to the Britannians, he protects her from them and allows her to maintain her cover identity, because he wants a chance to convince her to change her mind, though he promises never to hold back on the battlefield.
Also, I figure Tohdoh would've been there to have seen Suzaku's growing discontent with the JLF, and probably was there for the day Suzaku effectively split. Hence why his first reaction is accusing Suzaku of cowardice, but the moment Suzaku explains that, no, he's actually fighting for the people of Japan, just in a different way that does not involve terrorism, he not only immediately backs off, but understands and encourages Suzaku to go down that path. He doesn't seem to hold any kind of grudge against him for it, at least not until Suzaku becomes the Knight of Zero, when he feels like Suzaku abandoned the path he was on in a bid for power. Once the Zero Requiem comes to a head, though, he seems to understand what just happened, and also seems to recognize that Suzaku is the one wearing the mask. Which is why I think that, post-series, Tohdoh stayed with the Black Knights, serving as Zerozaku's Chief of Staff.
As for the Black Knights and Zero, I think that, had Lelouch bothered to unmask and straight up asked Suzaku to join the Black Knights (pre-Euphy/SAZ, mind you), Suzy probably would've declined. But rather than turn his friend in, he likely would've explained his position, and wouldn't have uttered a word about it to the Britannian military. He may have even bothered to explain this during his confrontation with Lulu after they killed Charles and Marianne. Especially since Part of the Zero Requiem is basically them taking the best of both their original ideas, with them "using the system" (or, more accurately, Lelouch using his birthright to take over the system) to change things, and combining it with Lelouch's underhanded theatrics and manipulation. With the Black Knights having gone legit by then, Suzaku would have few qualms being Zero, beyond the whole "thy must kill thy best friend" part of the deal, since he wouldn't be running a terrorist organization.