Oh my love, that is an awful lot to deal with :( It's no wonder you can't see the woods for the trees.
I am so sorry to hear about your Dad :(
You aren't a terrible Mum, bad things happen to good people. Your son has you, that is the main thing. That is the most important thing of all. There is no way he'd be better off without you. If you need any proof of that read the threads by MNers whose parents committed suicide or just pissed off. They are (in the main) broken people, it fucked their entire lives up. Others had it tough as kids (no money, rubbish housing, moving a lot etc, not much food) but had their parents - they are far more balanced. He would not have more security - he would grow up wondering why he wasn't good enough for his mum to stick around. He would wonder what he did wrong. You don't want that for him do you?!
Have you been to the CAB to see if they can help you with benefits/to pay the rent? Benefits for heating etc - there must be something out there to help you?!
DS is the only one who needs Christmas presents and they don't need to be expensive - just a few bits wrapped up.
Is you DP applying for every single job available? Now is not the time to be picky! If he is - good on him! If he isn't - kick him up the arse.
Can you find some work??
Don't worry about the neighbours - most will just be worrying about you, a few might be judging, the judgy ones are few & far between and can just piss off - they aren't important.
I don't know what helps you, but I find making lists helps me - a LOT. It gives you a feeling of control and also helps you to stop turning it around in your mind so much. Make a plan, decide what you can do to help yourself and start tomorrow, there's never 'nothing' that can be done to help.