Can a relatively skinny guy like me (9-12% body fat) lose fat while gaining muscle through fasting and eating healthy and weight lifting, or is it harder to do both at the same time if you're already pretty low-fat?

All of these thing dont work together,

Fast gove your less or no calories, weightlifting require huge amount of calories to lift, and you need protien to make muscles.

So fast will make you lose fat and then lose muscles, because muscles are also source of energy, your weightlifting will make you lose muscles.

Also eating healthy, what do you mean by that? Are you vegan? Thats what i hear mostly when people say eating healthy.

If you need muscles then eat meat, you need Protien to build muscles, also fat is good if you are weightlifting, because if you dont have fat then you will lose muscles as i said above.

So keep fat, eat meat, make muscles by weight lifting, once you have muscles then you could try to lose some fat, but not all. Fat is good.

I can do 20 something pushups easily but I can barely manage a few pull-ups. Why is this and how can I fix it?

Your ability to do push-ups and pull-ups have practically zero correlation to each other, so ignore how many push-ups you can do.Think about the muscles that are working when you're doing pull-ups, and then consider the muscles that are working when you're doing push-ups. These are 2 completely different groups of muscles.

Is there a difference between human and other life?

I think the answers that say "it's just how nature goes, lions kill zebras too!" are way too oversimplified, and is just a way of excusing our actions.The way I see it is that there are 2 stages at which a species can be.The first one where most lifeforms sit is the stage

Why do some gym members at my gym keep coming to me and trying to chat with me about their life then call me anti-social when I tell them I want to be left alone to exercise?

I've seen the type. They do a set and talk to others for 30 min , do another set , repeat. Lol, I know . Well for them it is a social event as mush as a workout . It may be the only contact they have with others