Hi Aaiiii, rising and falling intonation is important when you speak wrong intonation gives people wrong impressions. On the examples you have given: you can come with ME you can come WITH me - the second one the correct intonation. This is on a friendlier tone the first one.

aaiiiiiiiii, Yes, intonation is very important in English and can be very complex. How are you? This sentence can be stressed in several different ways. Here are a few examples. How are you? This is the normal stress pattern. The first and last syllables are stressed and the word "are" is destressed. The sentence has a slightly falling intonation at the very end. How are you? hOw'r yU?" How are YOU? This is how the sentence is stressed when someone returns the question to the same person who asked it originally. The sentence has a rising pattern because of the final extra stress on the word "you". A. How r you? B: Fine, thanks. How are YOU? How ARE you? This variation indicates extra concern about the person's health. Perhaps the questioner heard that you were sick, or he really, really hopes you are just fine! ------- You can come with ME. You can come with me in particular. Nobody else wants to go with you to the beach? Don't worry you can come with ME. I will be happy to be there with you. You can come WITH me. You can't go by yourself because they won't let you in the club, but don't worry, you can come WITH me. I am a very important person there and I will make sure that we go in together.