Translation:After that long day, they were worn out.
I think "cette" can mean both "this" or "that." But if it can't, then I'd love to know why!
It usually can but I think it may be skewed to that due to "they were worn out". "After this long day they were worn out" sounds odd to my ear.
"After this long day, they were worn out, but I was fine." This is perfectly okay!
If I am only hearing this, how can I distinguish between "il etait" and "ils etaient"
It's easy for this verb, because the liaison creates a "z" sound between the words (i.e., the "s" in "ils" is not silent). But most of the time, you can't tell the difference, except by context.