oh no! I'm sorry things are looking that bad. I can't tell you the relief getting my ILR was knowing that if something happened we'd still be ok.
In terms of jobseekers allowance, yes this is the job centre, you may have to go every week and 'sign on.' A co-worker's wife was made redundant and even with her payout, their savings and his job she still get something.
The local council will handle your rent and council tax. If both of you are made redundant, you should get full, if one of you is it may be less, it is worth applying either way. Where I am, the form is the same.
In terms of tax credit, if you google for a tax credit calculator you should get the official one which will tell you what you can can get in tax credit. Again, it is worth looking at this if only one of you is laid off as a decrease in income could result in a tax credit.
Your council may have a benefits help office to help you through this, again, I know mine does.
Good luck.