The best is living in an environment where the language you want to learn is spoken, in my opinion. The next best way I find is learning while being entertained (i.e. watching movies and TV shows).

Both are equally good and acceptable in both formal and informal emails/situations.

My ancestral language (Oromo) and my country's (Canada) languages use ABCs or the Latin alphabet as they're called. However, I was able to quickly learn Arabic because when I was in Ethiopia, I had the opportunity to be around a small community of Arabs who lived and worked there. They would even have me visit their local mosque (even though I'm not a Muslim). I was privileged to meet and interact with such good people which allowed me to learn about their language and culture. So in my experience, nothing trumps being in an environment where the language you want to learn is spoken. And when that is not possible, then try your best to speak with native speakers online on any platform you can find that works for you. Apps and other methods are great as well but I wouldn't rank them #1.

Actually, it is "بحبها" and not "بحباحا". Which means "I love it/her" and the masculine version of the verb is "بحبه / bahebbu" and some people write it as "بحبو" in the Egyptian accent. The reason it's feminine in your example is because the noun "حاجة" is feminine as you can see the "ة" at the end of it. If, for example, instead of "حاجة" he said "شي / thing" then the sentence would be like this: "ايه اكتر شي بتحبو في القاهرة؟" "What (thing) do you like the most about Cairo?" Hope that helps.

بما فيه has more than one meaning actually, and here it means (including).