UC and having to give up work

My mum, who I am a carer for, (memory issues) will soon not be able to be alone for more than half hour or so, Thus, I will be looking at having to stop working (16) a week.
It will be a huge cut to my income, loosing my wages. Mum comes first though, Will I be eligible to claim UC? I have about £2350 in bank savings as a fall back in case of emergency fund.
Our council tax is high too, as I took out a loan to build a granny house attached to mine, I have done one of those calculations online , suggesting I will be able to claim, and be able to get council tax benefit. No mortgage, When my husband died, we had a policy to pay off mortgage.
Few questions, bear with me my head is all over place at moment…
Do I have to leave work first or will they take my months notice as not working, as I am due 3 weeks holiday that I’ve not took due to pandemic.?
How long do they take to do a claim?
Will my savings exclude me?
I have never ever claimed benefits, and would not need to had the retirement age not moved. I am 61.
Any advice welcome.

I suggest you call the Carers UK helpline as you have quite a few questions.

Additional Elements of Universal Credit (UC)
All of these elements are means tested. The Department for Work and Pensions (DWP) adds up all the elements you are entitled to. This is called your maximum amount of Universal Credit. After that, your income is taken away from your maximum amount to work out the amount of Universal Credit you are entitled to.

Carer’s Element
You can get this addition of £162.92 per month if you are caring for a severely disabled person for at least 35 hours a week. You do not have to claim Carer’s Allowance to get this element.

Unlike Carer’s Allowance where you are prevented from claiming if you are earning above a certain level (£128pw for 2020/21), for the Carer’s Element your level of earnings does not prevent you from claiming. However, as the Carer’s Element is a part of Universal Credit (UC), which is means tested, your earnings and other income will affect whether you can get this and how much Universal Credit you are entitled to.

If you are making a joint claim, you can get a Carer’s Element each if you both qualify for it. However, you cannot be caring for the same severely disabled person.

Getting the Carer’s Element of Universal Credit might affect the benefits of the person you care for. It might mean they lose their entitlement to the Severe Disability Premium (SDP).