"I need one teacher" is not grammatically correct, just doesn't sound right. If someone asks you, "Do you need a teacher?" then answering, "Yes, I need one" or "Yes, I need a teacher" is okay. "a" is a particle that precedes something usually a noun: Take a bath, drive a car, eat a sandwich, go on a date, buy a computer etc "one" besides being the number is not a substitue for "a" and usually is used to designate a single item. I want a toy Which toy? That one.

One more thing I want to add to that. In popular culture people will occasionally use "the" in place of "a" in expressions. This is especially common in advertising, so I'll go back to the shop example. About any grocery you can find vegetables. However, a grocery specializing in vegetables that offers better prices may say "This is -the- place to buy vegetables." with an emphasis on the the. Although, we know you can get vegetables anywhere, by using the they are telling you that this location is far superior than others and thus you should shop there for vegetables rather than anywhere else. In pop culture there was a widely used term among young people in the early 2000s or late 90s or so where someone would say to a boy "You are -the- man." again emphasizing 'the' denoting that the person is superior to others and deserves this special recognition. (In reality this was just another way of saying "you're cool" or "thanks" among young people, but the use of this terminology is still under the same reasoning as the first examples)

This is a good question. The term "a" does denote singularity, but this is not the emphasis of the statement. For instance saying "I wish I had a dog." has a different meaning than "I wish I had one dog." Try not to associate it with one. Rather, it should be considered the alter ego of "the." 'The' defines a specific object, where as 'a' does not. "I want to go to -the- store." This implies a specific store. You know which store you want to go to. "I want to go to -a- store." This implies that you simply want to go to a store, with no specific store in mind.