First you have some good questions.
THERE IS NO SUCH THING AS TRUMPET CHOPS!!! The person who told you that does not know what they are talking about. Learning to play any musical instrument is a skill. Skills can be learned/taught. For the trumpet it realy takes someone who knows what they are doing. Just because they have a degree or an opinion doesn't bestow knowledge or experience.
You've be taking lessons and you only have a consistant G at the top of the staff. Your teacher didn't know how to develop your range/embouchure!! Was your teacher a trumpet player? If so I'm very concerned that a trumpet player/teacher couldn't help you. As Rowuk stated " after a year you should be able to hit a high C", seems to me that they didn't know what they were doing. I'm assuming they had no problem taking your money.
You say your mouthpiece says 3C but is not a Bach but a store brand. There are a lot of copies out there of Bach mouthpieces. Unless it has another brand name like Conn, getzen, Blessing, etc. it could very well be an inferior mpc. How can you tell. Go to ANOTHER music store (not the one where you were SOLD this mpc.) and try a Bach 3C, a Yamaha 14C4/3C, a Stork 3C, a Curry 3C. Can you tell a difference? If it plays better buy it. If no difference put it back. The size of a mpc has nothing to do with how high or low you can play. If your embouchure is properly developed you can play a high C on any mpc.
Your playing issues are fixable but it will take someone with a proven track record of developing you as a player. No tricks, no gimmicks. Just solid tried and true methodology applied in an intelligent way. In 32 years of teaching the only students of mine who didn't develop were the ones too lazy to practice.
The reason you have issues is not because you Can't learn to play, don't have the right lips, aren't tall/short enough, wrong eye color. It's because you had a bad teacher. A bad teacher is worse than no teacher.
Do you have a web cam? I can take a look at you for free. Let you know if you have any serious bad habits. or you may be just fine and need to play and stop listening to the young and foolish. You obviously love the trumpet and you deserve to be able to play it and enjoy it.