Are you saying if miners switch to Bitcoin classic (once available) or change the header file in their nodes we might end up with two chains?
If you did this today, your 2MB blocks would be rejected. Unless they run their mining operations hoping others switch their nodes to higher limit so that they can accept larger blocks, confirming each other.
Yes. Part of the forking process is producing blocks with a version of a certain number or higher to indicate support for the fork. Once enough of the last n blocks (usually 750 of the last 1000 blocks, but that changes depending on how much consensus the developer wanted) have that version number, then nodes begin rejecting any lower version blocks and then some time after the fork actually occurs. This allows nodes to know that a fork is happening and that the fork is supported. Then there is the grace period for people to upgrade so that when the hard fork does happen, there is consensus and the blockchain doesn't actually split into two chains that could survive.
Do not let these guys scare you to much. Hard forks should be embraced and they would only lead to a split if there is a significant amount of divergence on the matter. Therefore a split would only happen if enough people chose not to upgrade. This should be considered a positive thing, since it solves the problem of tyranny of the majority. The ability to split represents our right to self determination. The freedom to have the Bitcoin that we want, regardless of any minority or majority changing the code. Bitcoin is freedom, people are scared of this freedom. Trying to scare others to give up this freedom. Do not give in, embrace what Bitcoin is, embrace the genius of its design. The ability to hard fork exists exactly in order to resolve such disagreements, this is the governance mechanism within the protocol that ensures the freedom and continued decentralization of Bitcoin.
Hard forks by themselves are not bad. However doing a hard fork without consensus can lead to a lot of problems. The problem now is that there isn't consensus on what to do, so at this time, a hard fork is probably not a good idea.
The second point you brought up is false. After the split it will not be possible to spend your coins twice on the same chain. The chains will have effectively split creating two separate currencies, it does not make double spends possible, for you to say that is just baseless fear mongering.
He doesn't mean spend the same coins twice on the same chain, he means that with two chains, the amount of Bitcoin you have essentially doubles. If you mix your prefork coins with post fork coins on both chains, then you have the same amount of currency on both chains. You have double of what you had originally and can thus spend more than what you should have been able to.