Hi Amanda, welcome to the forum.
How much weight can a mini carry--- well that depends on the size of the mini, and how "stout" they are, and also how old they are. A horse that is younger than two or three years old should not carry any weight at all, as they are too young and their bodies are still growing. A fully mature horse can generally carry about 20% to 25% of it's own body weight, so if you had a 34" tall mini that weighed 200 pounds, it should be able to carry 40 to 50 pounds. Remember to include the weight of the saddle, if there is one. If you had a 38" mini that weighed 300 pounds, then it should be able to carry 60 to 75 pounds. It sounds to me as if your sister will be too big to ride a miniature, though she could ride a larger pony. (after all, she will keep growing so even if a larger mini could handle her weight right now, it wouldn't be able to in the very near future).
As for how much a mini will eat, that is easily figured out as well. A horse needs 1.5% to 3% of its body weight in feed per day (that varies according to the horse's current body weight, how cold it is outside, how much work it does, etc). So if you figure the upper amount, and you have a 200 pound mini, you would feed about 6 pounds of hay per day, and if your square bales were 60 pounds each, then you would need three bales per month to feed your mini.
It's very important that horses' hooves are trimmed correctly, so I strongly suggest that you would hire someone to trim your horse's feet. You could possibly eventually learn how to do so yourself, but it would take time. "no hoof, no horse" is very true, and there is more to trimming a hoof than just cutting off some of it.
I hope this give you a start on your research on getting a miniature. I also applaud you for finding these things out BEFORE you get one, that will be very helpful for both you and your future horse!