Shit situation. I remember student accommodation. I had it easy, but I did do a solo deep clean of the first place (entire house!) I moved in to in my second year. Didn't know any better. In hindsight should have got the agent to get a contractor in.
It sounds like the house wasn't viewed prior to accepting a tenancy agreement? Is that the case? Otherwise some of these issues would have been seen, I would have thought. Or the previous tenants trashed the place.
I suspect the decorating in September is fiction with the intention of getting you to back down by making it appear a massive ball ache for you.
You could keep pushing; the council can force landlords to make repairs. But what you think is serious disrepair might not be the councils definition. Damp is often just the effect of lots of cooking and clothes drying.
Not sure where there is going, except if you want to get this totally resolved it will take a large co-ordinated effort. It might be simpler to find another house, or suck this one up and make the basic repairs yourselves and buy a dehumidifier.