I'm so sorry this is happening to you and really hope things will get better.
Your landlord can issue an eviction notice, but so far hasn't which is the good news but I can completely understand how worried you must be after the way he has spoken to you (which is wrong and illegal). Regarding the rats and mice problem, you can go to your local council and report these issues to them directly (call them or check the website). The council will come and inspect and also fine your LL for this. They will get rid of the vermin and bill the landlord themselves.
Here are the rules about section 21/eviction for landlords: https://www.gov.uk/evicting-tenants/section-21-and-section-8-notices
Please note on there: the landlord cannot issue you a section 21 if they have not put the tenants’ deposit in a deposit protection scheme . I have a feeling your landlord hasn't does this, given the state of the property you describe (vermin). If they bring up that they will evict you, ask them which deposit scheme your deposit is in... I have a feeling your landlord can't legally evict you. Landlords lose all rights if they do not obey their end of the law. In addition, if he did try to evict you and you refuse to leave, he has to then take it to court for a court order, costing him money and time. If he has not done his part as a landlord, it is very likely the court would side with you, so do not fear this :) It may work for you. Please read that link above as there are many points on it that could work in your favour.
Having said all this, I think that it would be a good idea to make a plan for exiting this rental you are in. Since the landlord hasn't issued a section 21 "yet", you have some time to figure this out. Don't wait for them to kick you out, try to leave sooner.
Some options:
Save what money you can (I know this will be hard, but whatever you can save, save it).
Call Citizens Advice Bureau regarding help with housing, they are really food: https://www.citizensadvice.org.uk/scotland/housing/finding-a-place-to-live1/if-youre-homeless-or-at-risk-of-homelessness/
Call a Women's shelter and seek advice about your options and if they can provide a solicitor who can help with the CCJs (I am not sure if they can, but it might be a good place to start - also Citizens Advice may also be able to help):
https://refuge.org.uk/
Try OpenRenthttps://www.openrent.co.uk/ - there are usually quite a few properties on there where the landlord doesn't require a deposit or too much for a deposit, and they don't usually do a background credit check and will trust that you'll pay the rent. You can try there and negotiate rent amounts but don't tell them about your CCJs.
Contact your council directly - show up or call the relevant department about your landlord and threats to evict you with a child.
Another option is emailing/calling your local MPs (tell them everything), regardless of whether Labour, Conservs, etc. Just maybe call all of them and tell them about your situation. They will know for sure what local help is available and also can push for the council to help you too.
Lastly, it might not be something you want to do now, but perhaps you can contact your local newspaper about your landlord, or a bigger media outlet like The Guardian. If not now, you may want to consider doing this later. I would document everything with your landlord, keep all emails, if you speak on the telephone, followup with an email summarising the call, make notes in a diary and literally keep everything. You may be in a position one day where you can get compensation back from this God awful person. I also hope you find the right solicitor to advise you about the CCJs.
I don't know if the above is any help, but hopefully it's somewhere to start. You will be ok, you have to believe you will be. Please get some rest tonight and start fresh tomorrow. You can do this. Good luck