They are both correct! The one who prounces "year" to rhyme with "ear" is more 'standard' so, at this stage in your English studies, make more of an effort to imititate this teacher's pronunciation. Personally, I find the other accent ("year" to rhyme with "her", "cup" more like "cook") very beautiful - my wife and her family speak with this accent! - but, as a foreigner, and a beginner, it's best at this stage to imitate the first one.

OK, your first stop should be at the BBC website, then howjsay.com - these are standard pronunciations of English. Quite a number of British/Irish accents pronounce the neutral "u" (up) as an "oo" (oop). It's worth your while to find out which towns your teachers come from, as that will help you identify accents in the future. Most importantly, listen widely and find more examples of English speech - don't just rely on one or two sources.

First of all, there are many different English accents. However, there are some that sound more educated/correct than others. The classic British accent is called Oxford, so if you look that up, you should find some resources to help you mimic that pronunciation. If you listen to English language radio, try BBC (British) or NPR (American). To address the words you mentioned - "year" should always rhyme with "ear." Are you sure that the teacher who pronounced it like "nurse" wasn't actually saying "your?" "Cup" can either have the same vowel sound as "cook" or "what." (My preference is "what.") The "t" sound is tricky. Some people barely pronounce it at all in certain words, while others enunciate it very clearly. There is a phrase that refers to not pronouncing the "t" sound; it is called "swallowing your "t"s. The best advice I can give you is to listen to good news programs and make friends (on this website, for example) to practice with over Skype.