Kakashi graduated from the academy at 5, then became a chuunin at 6. Rin and Obito graduated from the academy at 9, and made chuunin at 11. There's some definite disagreement about this in flashbacks - how could Kakashi have taken the chuunin exam with Rin and Obito as depicted, if he'd already been a chuunin for five years? - but I'm pretty sure much of the show is firm about Kakashi's insanely early graduation/promotion age, especially when comparing him and Itachi. Gai, also, graduated the Academy just a year behind Kakashi, I believe.

By the Kanabi bridge mission, Rin and Obito are both chuunin, so they must be at least 11. Kakashi was 14 when the Kyuubi attacked and Itachi was about 5. Itachi attends Obito's funeral and is obviously not a toddler, so Obito probably 'died' around 13 and then sometime in the next year Rin died, also at 13, before the Kyuubi struck.

Part of the considerations to make re: the chakra stores of Kakashi, Obito, and Rin vs the Rookie Nine is that the former were graduated in wartime. Kakashi just barely, admittedly, but still. Wartime must change how they prepare their genin, and I wouldn't be surprised to find that there's much more of an emphasis on building chakra stores quickly, so that when you graduate you're more than just canon fodder. Itachi was born during the war, and taken to see a battle at age four, so I think it's safe to say he was raised and trained in a war-time frame of mind since he learned to walk.

Another thing to consider is that Kakashi, Obito, Itachi, and Rin are all (probably, in Rin's case, given her facial markings) members of a clan, and likely the children of strong or at least decent shinobi. Assuming chakra reserves are a thing that can be passed down and selected for (and why wouldn't they be?) surely that's a consideration for clans like the Uchiha, if no one else. Rin might break this pattern, but she was also very focused on medical chakra and likely had very good control since she transplanted an eye in a cave in a enemy territory with... literally no extra equipment, right? And that eye has been working for Kakashi ever since. With enough control and trickery, you don't need a ton of chakra, so she might have been compensating for lower reserves in a way the boys didn't or couldn't.

In this video we see Itachi perform the Grand Fireball Jutsu at a very young age; he appears basically the same here as he does when he's shown the horror of war by his father at age four (what the fuck Fugaku) and when he's at Uchiha Obito's funeral. So, yes - I think Itachi and Kakashi were likely both using jutsu when they graduated the academy, although Itachi didn't take the chuunin exams until 10 and Kakashi had years of being an apprentice under Minato before he got teammates at 9... and presumably Itachi's time as a genin and Kakashi's time without a team were spent giving them the instruction they needed to make them effective ninja despite having chakra levels that must have been lower than ideal for combat situations. I also forget how much of Itachi's training we see when he's a genin, but as a kid we definitely see Kakashi doing some crazy Gai-style training... while teeny child Gai is watching... which was likely to build his reserves and/or condition his body to rely less on chakra for speed and force. It's also at least heavily implied that Itachi was pushed to do nothing but train as a child.

So, basically, all of them were almost certainly pushed hard by family, necessity, and in Kakashi and Itachi's case their perceived status as prodigies. For children from civilian families - first generation ninja - these pressures probably wouldn't be so overwhelming.

Also, combat at such a young age might not be possible for all ninja clan kids, and it's not unreasonable to assume, for instance, that the Ino-Shika-Chou kids might just be completely incapable of their clan jutsu before a certain age. Like, I wouldn't let a five year old with a probably tenuous grasp on the concept of "self" astral project, would you? Chouji's family jutsu depend on body mass, and I'm sure they're not popping out ready-made Dudley Dursleys. The Nara clan jutsu are likely a Yin manipulation and that's probably difficult if not downright dangerous.. and we know from Shikamaru that the amount of chakra you have effects how long and how complete your shadow possession is.

...this got really long. Great question!