15 years ago my banding didn't change untill DD arrived and took another 11 months before I was able to move in to a property. Depending on the area it could take significantly longer than that now
Completely discount the child's father right now, he isn't particularly jn a place to be relied on, as soon as baby arrives go through CMS and they will work out a fair amount for him to contribute removing the emotion out of the situation and work out contact then too
You have a lot of things in your life that you can't control right now so make a list of the biggest things that are bothering you and do what you can to fix them. Make sure you are on any 'free' websites, trawling charity shops to put house and baby bits away for when you can move.
What type of bug infestation? Something easy to treat yourself?
Look at retraining whilst you have some time, even if it's something online as you see to have internet access there are many free courses or look at what is offered at your local library or skills Hub learn how to use Excel properly etc so that you have a wider choice of jobs when you go back to work
In terms of space even a hotel room will be ok until baby is mobile, it'll be rubbish for you but make no difference to baby. It sounds like you want a strong and stable future and you can have that it just depends on your decisions from this point on really.
You mention you were kicked out and sound generally very vulnerable have a look at what other support and charities are available in your area who might be able to assist you too. If you are under 25 a young mum's refuge maybe an option.