Ill try to make sure i answer all ur questions here.. 
""If I bred rats, would the fuzzy rats be the same size as hopper mice?""
fuzzy rats are "roughly" the size of full ADULT mice.. a pink rat is roughly the size of a "fuzzy" mouse.. give or take a few days of growth..
""And would weanling rats be the size of adult mice?""
weanling rats are roughly 30 - 50 grams.. sometimes larger depending on how many babies the female has.. where a "adult mouse" can be 10-30 grams in size.. so the answer is "kinda sorta" it all depends on when you pull babies for your snakes to eat..
""And how long does it take for a rat or a mouse to reach full size?""
im not sure what ur askin here exactly.. but ill go out on a limb..
how long until a rat is "weaned" and the same size as a adult mouse?.. and how long till a mouse is "adult" size?..
rats will be weaned at 4 weeks of age.. it will take a mouse at least 10-12 weeks to get to 'full adult size'.. so you can see how much better it is to raise rats 
""If I bred mice would I have adult mice when I needed them?""
that depends on how many mice you want to raise up to "size" for feeding.. remember.. more adult mice = more smell = more food = more mess!..
your yearling corn eats hoppers?... i have a yearling male corn who is feeding on large rat hoppers with no problem.. i convert all my animals to a rat diet as soon as possible.. i just hate dealing with mice! LOL plus ive noticed they grow so much faster on a rat diet
your yearling ball python should probably also be on small rats by now.. i have several yearling females and males who are all feeding on weaned rats with no problem.. 
best of luck
dan