The size of horse or pony you would require would depend a bit more on your weight than your height really. A horse or pony should never carry anymore than 20% of it's own body weight, this includes the rider, saddle and any other gear. At 133cm (4'4") you could ride just about any height of pony, from 12 hands upwards so long as it is able to carry your weight well. If you are still growing you would do better to buy a slightly taller horse than what you need now, as this way you will not out grow it so quickly.
The cinch size will vary from horse to horse, measure the horse where the cinch should be and that'll give you a good idea of what size to get.
It depends on the size of the horse.
There is no one size for a thoroughbred, you need to find the custom fit for your horse. To find out how to measure your horse for the saddle tree, see the related link.
At least half an acre. The size of the paddock will depend on how you intend to keep the horse. If you are going to use a 'drylot' system, then a horse needs a paddock around 100' x 50 to 70' (feet) in size. If the horse will be on limited grazing, then a quarter to a half acre would be better.
I would say pony size.
Depends on the riding level she is and how broke the horse is. Size does not matter. It all depends on the horses behavior.
A good size to get a girl toddler would be any size that ends in a T. When a size ends in a T it means that it is for a toddler. A decent size would be a 3T.
Cob or medium
I would recomend medium size. Im also in the market for splint boots, and I found the medium size is for horses 14'2- 16' HH or the average size horse.
A two stage 8 horse should do the job well, I would not get anything smaller.
Different breeds vary in height and weight. An adult Shire is far bigger than an adult Quarter Horse. So the size could be 68 to 88 (just an example) depending on the breed and build of the individual.
No, actually, she would be too tall. I know someone who is about that height and rides a pony that size, and her feet are nearly at his knees when she rides bareback.