When I visited Venus Fort, a very upscale Tokyo shopping center, I was surprised to see that not a single shop name appeared in Japanese. But a few appeared in International Phonetic Alphabet rather than the Roman alphabet. I saw this elsewhere in Japan as well.
I asked a similar question eight (eek!) years ago: Why is the writing on Japanese electronics always in English? - Factual Questions - Straight Dope Message Board
In the case of “bye bye” (Japanese “bai bai”), it’s a couplet in the original English.
Article about the influence of English on current Chinese:
http://languagelog.ldc.upenn.edu/nll/?p=4168
This is globalization, and it’s everywhere. Get used to it.
It’s not like English doesn’t borrow words from everywhere, too. It just doesn’t seem as unusual since we borrow a lot from languages that use the same alphabet as we do.
Though I admit actually using the Roman alphabet is different–even otaku (rabid anime fans) use the Roman alphabet, despite the idolization of everything Japanese. I think this comes from the fact that it’s easier to type. It’s easy for a Japanese person to type Roman letters–the keys are even the same. It’s much more difficult for us to type in any of the Japanese writing forms.
I’ve been here for 13 years and I can’t remember seeing IPA used outside of schoolbooks. Are you sure that wasn’t just some random diacritical marks to make things look more French/European?
Can’t speak to Japan. I live in Korea and a surprising number of TV ads are in English, mostly for upscale, expensive products. Fluency in English is often associated with brighter career prospects.
In one very odd commercial, a man and a woman are talking to one another, he in English and she in Korean.
I’ve been to Japan a number of times and have also never seen this. A screenshot would help. I suspect what he’s referencing is very stylized romaji or katakana.
So that young girls can advertise “I am a Slut” on the small of their backs in a foreign language that isn’t easily goggled by their parents. Really mom, I thought it meant Peace not Piece! 
Because English has this je ne sais quoi.
The Japanese football (soccer) league is called the J. League, in the Latin alphabet. I always found that a bit odd.