could L1/L2 cache line each cache multiple copies of the main memory data word?
No - if it's already in the cache the MMU will use that rather than creating another copy.
Every cache basically stores some small subset of the whole memory. When CPU needs a word from memory it first goes to L1, then to L2 cache and so on, before the main memory is checked. So a particular memory word can be in L2 and in L1 simultaneously, but it can't be stored two times in L1, because that is not necessary.
It's possible that the main memory is in a cache more than once. Obviously that's true and a common occurrence for multiprocessor machines. But even on uni processor machines, it can happen.
Consider a Pentium CPU that has a split L1 instruction/data cache. Instructions only go to the I-cache, data only to the D-cache. Now if the OS allows self modifying code, the same memory could be loaded into both the I- and D-cache, once as data, once as instructions. Now you have that data twice in the L1 cache. Therefore a CPU with such a split cache architecture must employ a cache coherence protocol to avoid race conditions/corruption.
Yes it can. L1 copy is updated but has not been flushed to L2. This happens only if L1 and L2 are non-exclusive caches. This is obvious for uni-processors but it is even more so for multi-processors which typically have their own L1 caches for each core.
It all depends on the cache architecture - whether it guarantees any sort of thing.