That is purely a software issue. Word size does not limit how big numbers computer can handle, it just implies how big numbers it can handle efficiently. Even lowly 8-bit computers/microcontrollers can do arbitrary precision/bignum math.

Not if you run an operating system/code with 64 bit time_t, like NetBSD or OpenBSD. I can't imagine you would run an OS on it though.

Probably not. These would be useful in wireless sensors and other devices where having an accurate absolute time is not as important as knowing precisely how fast time is ticking away. If I were going to use something like this I probably wouldn't even bother noting the absolute time of a sample at the point of measurement. Rather, I would just periodically synchronize the network with a clock pulse and let each individual node figure out whether they're running fast or slow, and by how much, if it even matters.

If it doesn't then just note the time of arrival at whatever server is controlling the network and use that time exclusively. Then you can buy one 64-bit machine and leave it running all the time, and as an added bonus you no longer need to worry about whether each node has the correct time.

Just because it's 32-bit doesn't mean its code can't store 64-bit ints. There's just a few more instructions that are needed to manipulate it. But it's not a big deal.

That's how computers are able to store, retrieve, and manipulate any variables (like strings) that might be bigger than their address space.

I'd rather use another degree of freedom: how small can I make my battery?