In the United States, children are taught to read in a mixture of two different ways: "sight reading," in which they are taught to recognize the entire word as a whole; and "phonics," in which they form the word from the individual sounds of each letter. Typically, phonics is used as a kind of backup or memory guide. Children are taught to try to recognize the word by sight, and then "sound it out" if they can't recognize it. English spelling is difficult even for native speakers because it is only roughly phonetic. In some cases the spelling preserves the way words sounded centuries ago. No spelling "rules" are actually reliable. The spellings of some particular words are very difficult for English speakers to remember and are often misspelled--so much so that I am glad the computer checks the spelling as I write these: separate, parallel, weird, sacrilegious, harass, embarrass. We do not learn any phonetic alphabet. Dictionaries will indicate the pronunciation using a phonetic alphabet, but they have to give a little key at the bottom of each page because the phonetic alphabet is unfamiliar.

I think there are two separate issues here; firstly the difference between a logographic script, like Chinese, and an alphabetic one, like German, English, etc.; and secondly the pronunciation of the language. The concept of the Chinese script is that each character depicts a word (or, rather, a morpheme), without regard to pronunciation (although many characters do contain some clue as to how they are pronounced); whereas in alphabetic writing each letter (ideally) represents a sound. Therefore, speakers of languages with alphabetic scripts don't need to learn a separate phonetic notation to tell them how to pronounce words: it's already evident from how the word is written (even in English, which is much derided for its irregularity, spelling does follow set rules and in fact the vast majority of words can be read correctly according to these rules). So in this respect, no, there is no equivalent of Pinyin for German, English, etc. As for pronunciation, every language has its own specific and unique set of sounds (phonemes) and when you learn a new language, you should try to pronounce these properly and distinguish between them all, even though the sounds and the distinctions made between them may be different to those of your own language. This doesn't mean that you necessarily have to sit down and study phonetics, it may be enough just to listen well and imitate the pronunciation of native speakers. If you don't master the phonetics of your new language, people may have trouble understanding what you say, and you may have trouble understanding what others say. However, just as you grew up pronouncing Chinese even before you could read, so English speakers pick up the sounds of their own language in childhood and do not have to formally learn them.

I think the main issue is that you're moving from one writing system to another, so phonetics helps you avoid bad guesses. However, I think if you're learning with good speakers of the language, you probably don't need phonetics to bridge the gap. For English, no we don't learn the IPA but we do learn pronunciation for own own alphabet, diphthongs and other rules such as for the silent e. The so-called exceptions are easier to find and understand as we learn more.

in German you basically speak just as you write and it's so in all European languages

If people need to read and write, they will learn phonetics. Otherwise, they don't have to for people around them can talk with him.