SSP run out, unsure about Incapacity Benefit

I had surgery for breast cancer in March and have been signed off work since then, just completed chemotherapy and am waiting for radiotherapy. My current doctor's certificate is from 1 Sept to 1 Dec.

My job is being held open. My contract is 20 hrs/week Mon-Thurs. My employer agreed to pay me my basic contracted hours until the end of September and said I would then go onto SSP, which isn't really a lot less than my basic weekly pay.

I'm a single parent. My youngest has just started 6th form and I rang the Child Benefit office early Sept to tell them she was still in full time education. They told me to let the Working Tax Credit people know too. The WTC office asked about my employment status and when I told them how long I've been off sick, they said I would have been getting SSP and it would stop after 28 weeks. Our wages office checked with the tax office and confirmed my pay had actually been SSP plus top-up to make it up to my basic pay, and yes, it would stop near the end of September, I'd then have to try and claim Incapacity Benefit.

I rang Jobcentre Plus to ask about IB and went through a 40 minute questionnaire on the phone. They said they'd send a copy of it for me to check and I'd have to take it into my local Jobcentre. That was 3 weeks ago, I rang yesterday to chase it and they'd got the address wrong, duplicate arrived today. I have just a few days now to take it to the Jobcentre as it has to be there within 4 weeks of my original call.

Looking through the list of things I have to take, they want proof of maintenance payments. My ex and I have been separated for 11 years, not divorced, and his payments are entirely voluntary, there is nothing in writing. He gives me a generous allowance and he pays the joint mortgage on this house. Since I've been off sick he has occasionally paid for the supermarket shopping, or filled my car, as extra help.

My son is 20 and on JSA, splitting his time between his father's home and here. My eldest is 22 and just started a new job, they ask for details of her salary and I don't even know what she earns. She does a lot of the shopping, and most of the cooking, but doesn't pay 'rent', though when her boyfriend is staying he does make a contribution direct to me.

Is IB means tested so that maintenance and my kids' incomes are reasons to refuse it? I'm not familiar with the benefits system, (can't begin to understand why for five years they've been clawing back what they say is overpaid WTC) and feel very sick and scared. I don't know how long it will be before I can return to work - it's a heavy manual job in a germ-ridden farm environment, which is why I had to stay off all through chemotherapy.

I still get Child Tax Credit, lost the single adult discount on Council Tax when my eldest left school and think the only other thing I can try for is extra loft insulation, which seems to be free based on CTC and my very low salary.

Any ideas appreciated, I have to sort this out next week.