Eek! The OU's website seems less than user-friendly for some things (especially when I've needed first to tell it that I'm in Spain and then later that I'm in England). However I agree that it seems that you can only take an access module while you're actually resident in the UK. What worries me though is that you might be required to provide a UK address when you
register for the course, rather than simply when you start it. I think that you'll need to enquire about that at
[email protected] .
It's not clear to me either what the requirement to be "registered on a qualification" (in order to study for free) actually means. Does it, I wonder, mean that you have to sign up to a 'full' OU course (to be taken after you've completed the access module) before you can be accepted onto the relevant module? (Again, I think that you'll need to email the OU about that if you're not already sure of the answer).
With regard to AirBnB though, any property that's available to let for 140 days or more in a calendar year is subject to business rates, so the property owner should pay such rates (rather than any occupier having to pay Council Tax). There's no limit upon how long you can stay in an AirBnB property except in any part of Greater London, where there's a 90-day limit.