SSDs store in large blocks, say 64k or 2m. The seek to get to such a block is constant if it's not in cache; the read time is constant if not in cache; so 'SSD seeks are free' is basically correct. However, sequential IO is likely to land on the same block, in cache, in which case the seek time is essentially 0.
In practice, on hardware I have tested on, HDD's have a 10x or more slowdown from random IO relative to sequential, while SSD's have a 3x slowdown. Your hardware is definitely not mine, take this with a Hummer-sized grain of salt.
I don't know anything about SSDs, so I won't address that. (Though, it might be the same as RAM.)
With RAM, you don't just say "Give me the 4 bytes starting at 0x10A6E780". Instead, a whole block of memory around that address is loaded into the cache (pausing execution in the meantime), and then the value is pulled from there.
If the next value you read is in that same block of memory, you don't need to spend time loading a new block of memory into the cache.
I worked with bare NAND flash on embedded system. NAND flash doesn't work like RAM where you have address pin that cover the entire space. For NAND flash, you have to send a read command with the address you want to read the data from. There are various kind of read command, one of them is auto-increment read, where you can keep reading the data and once the end of the block is reached it will load the next one.
random access just means that each access has the same amount of latency. It turns out that 100 nano seconds is quite a lot of time for a CPU. The CPU has to wait roughly 60-100 cycles doing nothing on a cache miss when it has to load stuff from RAM. If you have a predictable loading pattern like array[0], array[1] then the CPU can try to prefetch array[2] and array[3] since latency is the problem not bandwidth (unless you go multicore).
