Firstly, yes it freezes well and you don't need to cut it into pieces first. It cuts easily enough straight from the freezer.
Secondly, there are different types of chorizo, some are essentially raw (you'll find they're soft) while some have been dried/cured (they're harder)
They each have different uses and flavours (the raw ones tend to be saltier) but they should all be fine even after 10 days in the fridge. Hell, I think I've used chorizo quite happily even after longer than that.