helmet or face doesn't matter.
headshot is headshot = 1 shot kill.
No, you don't need to account for gravity, but if the target is moving, you do need to account for bullet travel time based on how far away the target is.
The crosshairs move around slightly while aiming, so you may not have been right on the head when you fired. And I'm not sure, but there may be some random deviation that means the bullet doesn't always go exactly where the crosshairs are.
To answer the original question,
Yes, you can play offline. But 90% of the people will tell you that online is what BF is all about.
The unexpected behavior of human teammates and opponents is what keeps this game entertaining.
Yes, there are some servers where you will find plenty of idiots who think it is great fun to run around trying to kill their teammates and destroy their own vehicles.
But you will also find some servers with good admins who immediately kick any of these idiots who try to join their server.
Once you have found a couple of good servers with regulars, you will have a great time playing a game filled with teamwork and strategy.
There are both SP and MP demos available for download.
They are fully functional demos each with one map.
The SP demo has one of my least favorite maps and I found it to be relatively boring.
The MP demo has one of the best maps (Wake Island).
I played the MP demo for about a month straight without ever getting bored of it.
So dl them both and give it a try.