Having read the description, no, she is NOT suitable for a beginner rider. Whenever the seller says that the horse needs a rider to continue her education, that means she is not fully trained. As for the 7yo beginner riding her, that would have been done in the safety of a riding arena, possibly on a lead rope or lunge line.
A beginner rider should aim for a well trained beginner's horse, about 13 years old (at this age the horse will have started to mellow and calm down- young horses can be pretty silly), quiet to handle on the ground and in the saddle (not all are), quiet and good to ride in company and alone while in the arena or out on the roads or trails. If the horse has been to pony club and horse shows, even better. The more the horse has done, the better it will be for you.
I myself have an Arabian pony (81% Arabian, the rest is welsh), and I got him when he was a 7month old weanling. Remembering back to when he was broken in, he was super quiet, but there was no way I would have trusted him with someone with little experience- green horses need a rider's full attention, and they are not great horses to learn to ride on. In fact, I still wouldn't trust him with a learning rider- he is the type who will take advantage of the rider's nervousness and try to intimidate the rider into getting off. He certainly has the attitude of the typical Arabian, he can be flighty at times, and he is smart. Too smart.
My first horse was a 12yo black nag gelding (no breed, but he did look a bit like a cross between a thoroughbred and welsh) who was missing half an eye. No one else wanted him due to that eye but he ended up teaching ME how to ride, and he is still the best horse I have ever ridden.
A proper beginner's horse will not do these things, they will tolerate the learning rider yanking accidentally on the reins, and what other mistakes the beginner makes, and there will be plenty. You need a well trained horse who will not take advantage of you when you start to feel off balance, or when you pay more attention to your position (readjusting your seat, the reins in your hands, the stirrups) than you do the horse. You need a horse that you will feel safe on, a horse that will teach you, and no young horse, no matter how quiet the seller says it is, will be able to help you learn to ride properly.
For that money, you could find (and buy) several horses that are more suitable for you to learn on.
You need a horse that can help teach YOU to ride, not a horse that has basic training that needs further training.
Other places to check for suitable horses are the Horsedeal magazines, through your local riding school (they may know of someone nearby who is selling a horse), people also post adverts for horses for sale at saddleries and horse feed stores, so check them out. Also, ask the people who work at the feed stores and saddlery if they know of anyone selling a beginner's horse- these people can be a great source of information about anything horse related.
Good luck with the horse hunting!