Answering Vayra's setting questions

 If you follow the OSR blogosphere you've likely seen half a dozen of people having done this already, but it really is a neat little way to solidify your own views on both your world and rules system which is why I too am joining in on the trend.
The original post by Vayra can be found here.

1) What class knows the most martial arts? Are they real martial arts like kung fu, or made up ones like krav maga?

Fighters are the obvious answer here. Rules-wise in LotFP fighters are the only people who progressively get better at hitting things as they level up and are considered to be people who already have some experience on inflicting violence upon others.
As for any martial arts, different weapons have distinct uses for them and while the fighting style might differ slightly between regions it's not really enough to be called different sorts of martial arts.
Clerics however are taught more non-lethal means of fighting as it is one of the teachings of the church to not harm fellow children of Varchic.

2) Can I start out having already made a deal with the devil or do I have to do that in game?

Currently there does exist a Diabolist class that starts with sharing their body with some sort of otherworldly being if that's your jam, but other than that you could start off as someone worshipping the Deep which is essentially a giant infinite leviathan's carcass rotting somewhere in the depths of the sea and plead your life to it.
Having interesting reasons to not turn back from life of adventuring is always good so I would more than happily work something out, but should you encounter terrible enough beings with enough intelligence you might also be able to strike a deal with one of those. 

3) Do you want me to write an 8-page backstory? Can I write an 8-page backstory, if I want to? If I write something down in it like I'm the timelost princess of the brass city and the daughter of the sun and I commanded legions in the Hell War but was betrayed by my father's vizier but I don't know that, or that I'm elf conan and cooler than everyone else, will that be true?

I would encourage not to write too long of a backstory as depending on how things turn out you might die faster than I can read through the whole thing, but if you aknowledge that you may lose this character in a sudden turn of bad events I won't hold you back.
As long as all those super cool and epic facts leave you in a similar starting position as the other characters -that is, near penniless and with having a reason to delve into danger for coin- then I don't see why not. I would tell you to work any major things through with me as to make sure it doesn't wildly break the world I've built up but as long as the tone matches the world it should be mostly fine.
I reserve the right to veto stuff from such novel, and you won't start with any tangible advantage over the other characters.

4) If I eat someone's heart, will I gain their powers? What about their brain?

In this world there exist dozens of old pagan religions with all sorts of beliefs and gods, as well as the Deep which is said to have been the state of things before land was formed.
If you have the correct rituals, invoke the correct higher powers, do either of those things by an accident, or eat someone deeply influenced by higher powers there is a fair chance that you will gain something.

5) These classes are boring, can I be one from somewhere else? What about from a different system entirely? 

If you show me another class that you'd like to play I can see about porting it to the system we are playing with, but if I feel like it'll break the setting or the type of game we're playing I'll say no.

6) If I make a sword, which one of us gets to name it?

You may call it whatever you wish. Wether or not that will affect anything will depends largely on the name and whatever situation you happen to find yourself in.

7) Am I allowed to kill the other player characters? What would I have to do to be allowed to? Do I win if I kill them all? Actually, how do I win in general?

This is something that would likely be atleast touched on in session zero with how do people prefer things to be, but at the very least you could be able to do opposing checks should any situation escalate to that point at which point Out Of Character it would be good to clear how the involved people are feeling about the situation before escalating it further.
While I expect the PCs to work as a team, any team will have the occasional conflicts.
Other than that, this is not the main focus of the game and killing other PCs will not result in any sort of victory or triumphant reward. There are no true victory conditions apart from having fun and any personal goals you might set for your character.

8) What language stands in for 'Common'? Or what are we all talking to each other in? Like the party, mostly, but also everyone else?

The world I've currently built is only one region so you'll be speaking the language of the common folks, the "cattle-herder dialect" if you will with no proper name to it.
Other languages might know or have heard of are Varchian, the slightly better regarded language that a lot of city-folks speak with much less dialectic differences and also spoken and written by nobles.
Third one is the church language heavily resembling Latin that is mostly used for sacred texts or sermons and mostly only known by nobles and church officials.

9) How do I learn how to talk to rocks? No not once a day just, like, normally?

Some of the old pagan religions might know spirits of soil or earth that you could converse with should you learn to see them, or by going deep underground where the common sense and civilization have not reached and even more primal existances dwell that you could learn things from should you not die on your journey towards this knowledge.

10) Which kinds of wizards get to serve kings and live in towers and shit and which ones are run out of town or stoned to death in the streets? Can I be both? At the same time?

Church and religion have quite a strong hold within the lives of people and thus have more influence than magi who are more from academic backgrounds.
Those who've either evaded suspicions from the church or lead rather boring and non-magical researches do often like to isolate themselves from the questions of the lesser learned folks of academia and some may even be employed as advisors for nobility. On the other hand, those magi pursuing more out-of-this-world subjects are always at the risk of church learning about it and dragging the magus away in their sleep, so they too do want their privacy by whatever means they choose to employ.

To be a magic-user who would get stoned as they pass by common folk would be to live somewhere where the church won't simply come and make you disappear. A modern scholar seeking solace amongst pagans of the old world, or a hermit living in the woods that gets regarded as a witch by the local villagers perhaps.