Firstly - stop beating yourself up for something that you had no control over. You are in a foreign place, living alone AND dealing with a tramautic, unexpected breakup. Those factors, on their own are pretty stressful situations, so be more compassionate to yourself. Yes, things could be better, or you could be handling things better but couldn't we all?
There is no timescale for getting over people. Some take weeks, some take far longer. Because it was unexpected, you are lacking closure from the relationship; the checking out period should be where you were able to control what happened too, instead of your partner calling the shots. Instead, like you said, it happened within 10 mins.
Perhaps he is suffering from a mid life crisis. He has been diagnosed with depression, but that doesn't excuse him behaving inappropriately. You ex should NOT be inviting you back to his bed, telling you he still loves you/appearing sincere and then 'dumping' you all over again. I suspect you are allowing it to happen for two reasons; 1) the breakup was not what you wanted/feelings or hopes may be still there and 2) your confidence is at an all time low - in the past you'd recognise the pattern of make up/break up sex/affection but now, you'll do anything to make it like before? Either way - your ex should not be indulging this. It is causing your emotional turmoil and is shifting the goal posts each time he contacts you, and that is not fair. Alongside this, he's also allowed you to become financially worse off from him leaving - although I understand depression is very difficult to manage, it doesn't give someone the right to cause you both emotional and financial distress. It does happen and it may not be his intent, but he is still facilitating your mental state, which sounds very much like depression to.
I know this may not be what you want to hear, but are you in denial about other women? People can, when needed, be decietful; your ex is already putting his own needs above yours by leaving you. He may see you struggling and feel that if he was to admit to other women it would make you feel worse. He isn't being considerate to you now, at the very least.
As for your relationship with your son; he is probably going through his own emotional distress at losing his 'real' Dad - it's an alienating situation, especially if a boy loses his father figure, the one who is essentially guiding him. So please do not blame yourself for your son's reaction - the person who should be accountable first and foremost is your ex - has your ex spoken to you son, or explained his decision? It sounds like you both need to heal, together and in your own ways.
Your son would NOT be better off without you. He would have lost TWO parents, and would be in a foreign country. You need to stick together and become a team - you'll have bad moments and there may be harsh words said, but your son needs you and you need him.
Practical steps - I'm not a lawyer/solicitor and not sure what country you are in.
However, if you have any joint assets, I would look at dividing and establishing who gets what, or who pays what. Speak to someone in a legal manner, get some advice too. I would then insist that if your ex needs to contact you, he does so through letter. No more e-mails, texts, social media, phone calls (unless urgent). Block, delete but before you do, I would instruct your ex that this is your plan, and for you both to move on you need him to comply. He'll probably beg you not to, but as weak as you feel, you can only get strong by acting strong initially, even if you don't feel it. Eliminate any situation (within reason) where your ex can just "pop" back into your life.
Go to your doctors about your mental wellbeing. Antidepressants need not be a long term option, but may help you get by for now. It is unlikely that your son would be removed from your care unless he was at significant risk of harm or neglect - as much as you think you are not doing a good job, you are doing what most people would be doing in your situation.
There is hope. There is so much hope - right now you are wounded, hurt, angry and confused about where you will be going next. You are in a position to do what you need to do to make you happy - the happy go lucky person will return and as with any challenging life experience, we usually learn a few things.
I hope nothing I've said has offended or upset you. Some of it is probably clinical, but you deserve to hear what may help you, even if initially it seems hard to read.
Best wishes 
(and sorry for the length)