I would never put side reins on a 3 year old, particularly to ride. At 3, all I want is for the horse to go forward, to stop and to turn. I don't even give a second thought to where it's head is. Side reins do nothing for the horse's back unless they are more advanced in their training and have learnt to swing over the back. I'll use them on the lunge so that I have a contact to start developing that swing, but at 2 or 3, it's go and stop only.
It's still a baby at 3, racehorses are bred to mature faster than other breeds - plus most break down very early due to this intense work as a young horse. Don't go by what racehorses do when training your own horse.
As a baby, you absolutely do not want to fry their brains. Keep the work easy, light, and short. Keep a nice soft elastic contact on the bit, and just expect the horse to go forward off your leg, and stop to your rein.
As they get more advanced I would expect to start training the horse to stop from the seat, but as a baby, leg means go, rein means stop.
Spurs, again, I would not put them anywhere near a 3 year old. It should not need them. I will only introduce spurs to a horse when I am beginning lateral work. Otherwise they're just unnecessary. Any reason why this horse is being ridden in spurs? Teach it to get off the leg only, and ride with a whip to give a reminder if the leg does not achieve an immediate reaction.
I also would not be jumping at all. Trot poles and very small cavaletti maybe, but not jumping. She's just asking for this horse to develop tendon and joint injuries. Hacking out for reasonable distances is ok, but keeping it to a walk/trot and minimal canter.
Many people (if they have a brain) will not buy a youngster that has been pushed exceedingly hard from the get go, as it's common knowledge that this can cause degenerative issues AND fry the horse's brain. Great if they're willing - but I've seen 2 and 3 year olds offering piaffe and flying changes, the rider has gone 'oh great my horse is talented' and training harder and harder. By 4 or 5 the horse has broken down physically and mentally and can't do anything other than pleasure riding. If a horse is willing as a breaker - keep it that way!! DON'T abuse that willingness or it will come back to bite you in the butt.