There's no point in your Mum calling, they can't talk to her unless you have authorised them to do so in writing.
Your council tax is charged annually not monthly. The period goes from 1st April to 31st March. Your bill should arrive in March and it generally splits the bill into 10 monthly payments so you pay from April to January and have two months off. You can ask for your payments to be split over 12 months.
Only adults count for council tax purposes so if there is only one adult in your property you automatically get a 25% discount.
The problem is that when you have council tax reduction (it's not a benefit it's a reduction) and your circumstances change during the year, you end up with less time to pay the new amount because the months left to pay are reducing and they have to give you two weeks notice of the new amounts. If you are paying by dd, it's very easy to miss a payment date during the recalculation and a small increase can end up with large payments due at the end of the period.
If your council tax keeps changing it's likely to be because HMRC have sent notification that your income has changed.
The council tax for the year (from 1st April 20 - 31st March 21) needs to be paid by 31st March 21 and most councils will not let payments go over to the next tax year because your new bill starts on 1st April and that will be harder to pay if you are still paying last year's bill.
The exception is if they take you to court and get a CCJ, then they will accept small payments. If they go down this route make sure the payments you agree leave you enough to pay next years council tax.
CAB will be able to advise. Alternatively call the council tax team, stay calm, ask them to explain the changes, tell them why you are concerned that the changes are wrong and ask them to recalculate or talk you through your options. They should be able to help, providing you don't kick off at them and they have people answering the phone who know what they are talking about. (Unlike my local council who have given all the reception and customer service staff half a day's training and put them on the council tax phones!)