I'm getting even more confused now, OP.
While your rent may be due to be paid 4-weekly, UC will work out how much that is equvalent to for a calendar month using this formula (weekly rent * 52)/12.
Did they say you would get rent paid in October and then not pay it? If so, you need to ask them why they have not paid the money you're entitled to. Or did their UC figures for October not include any money for housing costs? If that's the case, you need to ask them why you weren't entitled to it.
I also wonder if working that one week has cocked things up, too. Did they use the right figure for your earnings in November?
I think you need to go to CAB or ask to see a financial inclusion officer at your HA to get to the bottom of this. They will need to look at your UC account so they can see exactly how the DWP have calculated your entitlement from October onwards. Then they will know if the DWP have made a cock-up, not had the right information etc.
The UC system doesn't actually get its sums wrong (it's shit, but not that shit lol). Errors are usually caused by the wrong information being used. The calculations themselves are pretty clear, you should be able to see what income figures and allowances have been used and if they have changed from previous months.
It's also worth pointing out that just because a payment doesn't show as received on your rent account doesn't necessarily mean it hasn't been made. There have been endless problems with UC rent payments, and it is causing much swearing and gnashing of teeth at the HA I work for.
Please go and see someone who is a specialist in this sort of thing, and they will help you straighten it out.
You could also google "floating support" and the area you live in. Floating support services help people with issues that affect their tenancies and there may be one in your area that can help. Or your local council may have a homelessness prevention team who could assist.