Wow,this is a complicated one.I will try my best to explain but don't expect you can get it all just by one explanation,you have to have linguistic instincts for this. First of all,in most cases ,the adj+noun format is correct both with or without 的,unless you want to put some stress on the adj.For example,A：That is a girl B：Not just a girl ，she is a BEAUTIFUL girl。 In this case，A：那是个女孩儿，B：一个（漂-亮-的）女孩儿，in this case it is better to have a 的 instead of without it.Otherwise I think it is mostly right both ways,with 的 or not.But with a 的 ,it makes things more formal.And I will elaborate a bit more on your examples. Both 漂亮的女孩儿 and 漂亮女孩儿 are right,and basically mean the same thing.The very subtle difference it is more formal with a 的 ,so when you write stuff ,better with a 的. 好吃的美食 sounds fine,but 好吃美食 ...a bit awkward to my ears ,if not necessarily wrong.The third example you gave is even trickier,both being correct,but having different stresses slightly. 中国老师 stresses that the teacher is from China,stressing the ethnicity or citizenship.中国的老师 sounds more stressing the teacher China has.Like when doing patriotic propaganda you have.But it is a very subtle difference and can be used interchangeably without causing confusion. The reason I explained your examples is because there probably is not grammatical summary on this,even if there is one,99.9% percent of Chinese people don't know it.But I can feel whether something sounds right or not with or without a 的. I humbly advise you to pay less attention to grammar and devote more effort to osmosis,Chinese people are in every corner of the world ,try to find some and talk to them ,that will be much more helpful than analyzing grammar.I hope I haven't bored you by writing so much.And best wishes to your Chinese learning.

The way Chinese adjectives are formed is not that much different than some of the English words, like Beauty -> Beautiful, Mouth -> Mouthful, Hand -> Handful. In many cases the 的 can be omitted. 中国老师 = Chinese teachers 中国的老师 = Teachers in China But you are right, in many cases there isn't that much difference. By the way 中国老师doesn't mean Teachers who teach Chinese, if that's what you meant you have to say 汉语老师。 For the most part only Children say 我妈妈, 我爸爸 , adults normally say 我妈, 我爸, which is very informal. 很好的书, the adjective here is not 很好的, but 好的, which is the conjugation of the noun 好. 很 is an adverb. It's like saying "A very beauti ful girl" in English. 很美丽的姑娘 It's easier if you think of 好书 as a noun, although it really just means 好的书. 汉语书 is like saying Chinese books, all books written in Chinese are 汉语书， but what you really want to say is a book teaching Chinese, thus you have to be more specific and say 学习汉语的书 instead.

I think if you are speaking about a person you dont need to use the 'de' construct 我妈妈， 我爸爸， 我朋友， 等等 i am not native so dont take my work for it mo

2-1 -------------This is a tricky problem. Let me say, most native Chinese speakers cannot（maybe none could) give simple, plain and satisfactory rules for this problem, though on particular occasions we ourselves would choose the correct form(with or without the 的‘de’）without pains, and we would find with ease where there is a redundant or a lost 的'de' in a sentence made by a foreigner. Maybe this ability just comes from so called 'sense of (one's native) language'. ----------- Actually there have been a lot of articles treating of this problem, unfortunately, the exact answer is still staying open; but then, to sum up the major researches, I'd like to say that this problem is not about GRAMMAR, but about PROSODY of Chinese language; rather, it's a problem of prosodic(or metrical, or rhythmic) grammar of Chinese. In the following replies, I'll try to examplify the prosodic(rhythmic) rules on when the 的'de' is neccessary, when unacceptable, and when optional.

no exception you can always make adjective ＋ 的 + noun