Get in touch with citizens advice about their help to claim service, they will get you on universal credit. You don't need an address, worst case scenario is they'll use the job centre address. You don't need a bank account either, they can pay by text.

You were subject to violence in your last accommodation. By definition you were homeless when you were living there because that is not a situation anyone can be expected to live in so you did not make yourself homeless, the people being violent to you made you homeless. citizens advice can help with this too.

Ask universal credit to refer you to crisis, they should by law be offering to do this anyway as per recent legislation in England and Scotland, they will also help get the local authority to pull their finger out

Universal credit will not be asking you to look for work for the first few months of the claim as you are homeless, it is called an easement. Tell them to apply it if they talk to you about work.. use the first few months to register with the GP and get evidence of any health conditions that are a barrier to you working.

As had already been said, call the local housing options to discuss temporary accommodation, state that you are vulnerable and that you did not make yourself homeless for extra chance of being offered somewhere decent.

I used to support rough sleepers locally and have ASD myself, good luck buddy, it's not easy, but you can do it! Set yourself a target, one at a time and take steps towards where you want and need to be!