For such a "lingua franca" the pure number of speakers is not quite as relevant as the distribution of those speakers. According to the numbers (https://en.wikipedia.org/wiki/List_of_languages_by_total_num...), approximately 14% of the world speaks English as a first or second language as well. More importantly, English has 400 million more speakers who speak it as a second language when compared to Mandarin, which suggests that its speakers are more widely distributed on Earth.
While I agree with your viewpoint and it stands up on it's own, I also think it's important to remember the number of people that know at least 20 or 100 words of English. Simple statements can help at a lot of places, whereas I only know a single Chinese word. The number of people that can say basic numbers in English or very simple statements is much higher.
No. The proportion of the world's population that speaks English is greater than the proportion that speaks Mandarin. Mandarin is the language most spoken as the first language (and that's actually very debatable). This is irrelevant for choosing a language for people to speak with each other.
