Americans follow the rules, but their grammar rules. That's why there are students who study American English, British English, European Portuguese, Brazilian Portuguese, Spanish from Spain, etc. Although the variants are supposed to be intelligible, the grammars are not 100% the same. "Speakers of American English generally use the present perfect tense (have/has + past participle) far less than speakers of British English. In spoken American English, it is very common to use the simple past tense as an alternative in situations where the present perfect would usually have been used in British English. The two situations where this is especially likely are: 1. In sentences which talk about an action in the past that has an effect in the present: American English (AmE) / British English (BrE) Jenny feels ill. She ate too much. (AmE) Jenny feels ill. She's eaten too much. (BrE) I can't find my keys. Did you see them anywhere? (AmE) I can't find my keys. Have you seen them anywhere? (BrE) 2. In sentences which contain the words already, just or yet: American English / British English A: Are they going to the show tonight? B: No. They already saw it. (AmE) A: Are they going to the show tonight? B: No. They've already seen it. (BrE) A: Is Samantha here? B: No, she just left. (AmE) A: Is Samantha here? B: No, she's just left. (BrE) A: Can I borrow your book? B: No, I didn't read it yet. (AmE) A: Can I borrow your book? B: No, I haven't read it yet. (BrE)". For more information: http://www.onestopenglish.com/grammar/grammar-reference/american-english-vs-british-english/differences-in-american-and-british-english-grammar-article/152820.article

1) Nobody "follows grammar rules." We just speak. Teachers, linguists, and philologists study the way the language exists, search for, and discover consistent patterns, but they are not really "rules." 2) Be skeptical about things you read about "US versus British English." They are not wrong, exactly, but they are usually exaggerated. Many supposedly "British" usages are quite common in the United States, just less common than the "American" usages.

American English and British English are intelligible to one another. Any American would perfectly understand; Did you have lunch yet? / Have you eaten lunch yet? I just saw him? / I have(I've) just seen him

There are multiple varieties of English (British, Irish, Australian, American, Indian, ...). The differences are relatively minor. google "what are the differences between British and American English" will give you lots of material to educate yourself. To get started, I recommend this italki discussion: https://www.italki.com/discussion/170637

American English DOES follow grammar rules. I suggest you learn the difference in meaning and use between the simple past and the present perfect tenses before you criticize American English. In some cases, the difference between the two tenses is insignificant. In other cases, it's signficant. Did you have lunch yet? (simple past: a question of fact in the past) Have you had lunch yet? (present perfect: The difference in meaning is negligible. The question is still relevant now probably because I want to know if you're hungry so I can offer you food. I can also ask this in the simple past with no real change in meaning.) I just saw him. (simple past: a statement of fact in the past) I have just seen him. (present perfect: the statement is relevant to now, probably because in our conversation you said that you hadn't seen him, so I told you I just had.)