Yeah, a lot of people, especially younger people (including myself in the past) have used "and me" as it sounds fairly correct, but our grammar teachers were always correcting us to use "and I" instead, as it's essentially the proper phrase, but it probably sounds strange to a non-native speaker, but either phrase should essentially do the job, the point is still the exact same :P
As for the"Went home" and "come home", it's no big problem, you could even change one letter and say 'Came home" and it still make sense.
As for your last quote, it's perfectly fine, since you learnt about Michael Jackson's death when you returned from the holiday, although he actually died while you were on the holiday, one month is still considered fairly recent. Your English really is great overall, honestly if I didn't know that you weren't a native speaker I would never have even realized![]()