Benefits query after redundancy

Hi, hope someone can give me some advice.

After nearly 6 years of working P/Time, i have gone thru the redundancy procedure with my company, my last date is 12th June. I am ok with this, and as far as i can see, the company have gone thru the correct procedure and i am entitled to 5 years redundancy pay (which is not much as only part time hours). I am a single parent who gets Working Tax Cred and Child Tax Credits. My daughter is also eligible for DLA due to some disabilities and i get help with rent and Council TAx.

My questions are:

When claiming JSA or Income Support, do i have to advise them of how much redundancy i got, and will they reduce the JSA if i do?
A friend has asked me to help at her restaurant for 3 hours each week @ minimum wage (as she is pregnant), do i have to advise this and get a wage slip (as cash in hand) - will this affect my JSA?
Due to not working 16 hours now, i think i can claim for the carers allowance for my daughter, as below £99 threashold, is this correct?
DO i have to wait till my last day of work to contact the Job Center or can i call before hand?

Many thanks
Karen.