Not only are different cores allowed to read from the same block of memory, they're allowed to write at the same time too. If it's "safe" or not, that's an entirely different story. You need to implement some sort of a guard in your code (usually done with semaphores or derivates of them) to guard against multiple cores fighting over the same block of memory in a way you don't specifically allow.
About the size of the memory a core reads at a time, that's usually a register's worth, 32 bits on a 32bit cpu, 64 bits for a 64bit cpu and so on. Even streaming is done dword by dword (look at memcpy for example).
About how concurrent multiple cores really are, every core uses a single bus to read and write to the memory, so accessing any resources (ram, external devices, the floating point processing unit) is one request at a time, one core at a time. The actual processing inside the core is completely concurrent however. DMA transfers also don't block the bus, concurrent transfers get queued and processed one at a time (I believe, not 100% sure on this).
edit: just to clarify, unlike the other reply here, I'm talking only about a no-cache scenario. Of course if the memory gets cached read-only access is completely concurrent.