For #1, if I mine on one fork, doesn't that fork immediately become the one that will get most likely get accepted by the network?
If a) the protocol foresees a "first seen"-rule that prefers blocks that you received first
It is usually based on difficulty. Not a first seen basis. It does I suppose have an element of first seen, in that you can only orphan so many blocks.. usually 6 or 12 at a time.
If so why even bother with mining on both?
As I explained in the probabilistic approach, you don't even have to actually mine on both and send two blocks. It's even extremely unlikely that you will succeed on both. To maxime your chances it suffices to just check and see if you can mine on any of the two blocks, no matter which one you received first. Such a behaviour can distrupt consensus.
If you are within the same modifier interval, then it is actually extremely likely that you will get the same stake kernel on both chains. Why wouldn't you?
For #2, when is this attack used, during initial block download? Is the idea to use this stake to try to perform a stake grinding attack in advance and send those blocks to a syncing node instead of real chain?
Ideally, you would try to buy coins from early adopters when the coin wasn't popular already. That should make it "easier" to buy keys representing a large precentage of stake that existed at that early stage. However, as pointed out in the NeuCoin paper I cited, even if you possess a majority of historic stake it seems that you still have no realistic chances to win the battle since you'd still have to compete with 100% of the stake.
This only works if the coin has never had any checkpoints added to it. And even if it hasn't had checkpoints added, then it would have to be a coin that uses coin age, which a lot of the modern PoS clones don't do.
Really all you have to do is add a checkpoint after the coins have had a decent distribution, and then this argument #2 is pretty much void.