It is fine if you are speaking informally. It is informal (in other words, not completely grammatically correct, but often used) to use 'other's' at the end of a sentence like this. If you were saying this in formal language you would have to say "Why do I keep comparing my life to the lives of other people?"

The primary reason [for] sports [is] that [they] keep us physically and mentally fit. Nowadays, more people [are] facing job stress and health issues in their lives. However, we can manage [these] issues [using/by playing] sports. Playing any sport [will] decrease your body fat [and] also make [you] relax.

"That on you" is an informal, often joking way of saying "that is your fault", I think it's probably short for "The blame lies on you". E.g. "I didn't know it was your birthday!" "Well that's on you!" Implying that they should have known or found out. Maybe also as GuideDogSaint says, it could be used to say something is your responsibility, e.g. "Someone needs to bring drinks." "That's on you." Although, I don't think that is common. "It's by you" sounds very weird to me, I don't really know in what context you would say that, except for literally, e.g. "Who is this article (written) by?" "It's by you!" Maybe it is just not used in my part of the world.

I don't know if this is the same everywhere, but in Australia 'medic' can be used as a shortened word for 'paramedic', meaning someone who gives emergency medical care, often working in an ambulance or the army.

You are right, 'flying' is correct. I'm not sure I can properly explain why- I think it's because the verb "to see" is already in the past tense (saw), so the second verb is not. Normally you'd use flown only with has/have, e.g. "I have flown to England many times" or "that bird has flown back and forth five times now".

It definitely makes sense, though to me "now" doesn't sound quite right at the end of a sentence like that, unless you really want to emphasise it, for example if you had asked yesterday and things are changing really quickly, and so you want to know the situation right now. I'd usually use "at the moment" instead if the question is more casual, and so I don't really want to emphasise the "now" but just ask generally what the situation is like.

I agree with Jacob, though I would add that 'whom' is very rarely used today. It is used sometimes in formal written language, but it isn't used much in spoken English as it is seen as quite formal and old-fashioned. It can also be used a bit differently from 'who', for example in the sentence 'whom/who do you talk about' either is fine, though 'who' is less formal, but you could also say 'of whom do you talk' and in this case you couldn't use 'who'.

I would go with 'where are you coming from?', or else 'where did you JUST come from?'. You might also say 'where HAVE you come from?' You're right, 'Where did you come from?' indicates surprise, and while you could probably convey differently with your tone of voice, it still doesn't sound quite right to me.