You never lose bitcoins because you run a non-mining node.
This is wrong in so many ways, you obviously have no clue.
Of course not. Whatever happens on a non-mining node doesn't alter anything on a block chain (apart from sending goofed transactions eventually).
Dude, I explained several ways. Don't tell me not just because you don't understand them.
Secondly, there are several ways of losing coins due to a fork. Just see the mess that occured when Ethereum split in ETC and ETH. A chain fork can even be designed to steal coins or reverse transactions, like it was in the Ethereum case.
Forking happens by miners. And as long as the original chain is one of the prongs, your coins exist of course on the original chain. You are perfectly right that the ETH fork (by miners !) was done to reverse certain actions by one participant (the "dao hacker"), but he kept his holdings on the original (ETC) chain.
No, miners can't make a hard fork on their own.
Note that the forking is done by people building block chains and in a PoW system, these are mining nodes. Non-mining nodes cannot alter the block chain, and hence cannot alter any protocol, or any block chain contents ; as such, they cannot "lose coins". If by running a certain non-mining node, you've "lost coins", you can easily get them back: erase your node, and start another one with the "right" protocol (the one that can read the chain that has your coins out there).
Sorry, you don't make any sense. Please go back and read how you can lose your coins in a chain split. There will not be one blockchain, there will be two. If you e.g. spent your coins in one of the chains, and the receiver copy your transaction in the other chain, you have lost coins in the other chain. If you receive coins in one chain, the coins may not be valid in the other chain. In both cases you have lost coins. Erasing your node and reinstalling it won't get your coins back.
You should try to understand what a hard fork is. Miners are making two different chains from a certain common block onward. In a bilateral hard fork (the simplest to understand), the rules that say that a block is valid on one of the prongs, say that a block is invalid on the other prong and vice versa.
Whether other nodes copy these data blocks or not doesn't matter in fact. Miner pool nodes are building one prong, or the other one. Without them building these chains, nobody can get them, and the ONLY chains they can get, are these two chains because nobody is making any other one (by definition of "non-mining").
As a single chain defines a coin (by the creation and transaction rules on that chain), after the split, we have two different coins, which are just as different as bitcoin and litecoin. Satoshi has been mining bitcoin all by himself for quite a while in the beginning, so a miner can very well make a block chain without any non-mining node being around. No other node was around at that time, and nevertheless the bitcoin chain was made at that point. Satoshi could have made some fun, and could have made a hard fork at a certain point, making two prongs, and continue mining on the two prongs. If those two prongs would have continued up to today, we would have had two different bitcoins. Whether non-mining nodes were looking at that time or not. So, Satoshi, all by himself, could have made a hard fork, and two coins emerging from one.
There wouldn't be any other chain around apart from these two chains, with a common origin. These chains are, by definition, made by miner nodes (chain builders). And nobody else is needed ; and nobody else can make anything else without, himself, becoming a miner.
Of course, you can "lose coins" if in one of the chains, there's a rule that denies the existence of your coins. But that was the protocol that miners used to make that fork. Not your node's fault. If tomorrow, bitcoin is split in two, and in one of the two forks, my addresses are considered spent, then I lost my coins. But that is because the miners that decided to build that forked chain, decided so. Not because I was running a node or not.