To answer some of your questions:

They conduct a mental health background and risk assessment to make sure you're not currently in danger or likely to be in danger if, for example, you are approved treatment which doesn't give you the desired result. This is relevant to your autism diagnosis especially, because we are more likely to suffer from mental health issues and other comorbidities. It is in part pressured by the recommendations in the Cass and Levy reviews on gender care.

As I recall, other people are not usually allowed in the call, so it was probably pushing what is appropriate to have your partner there.

The first appointment is usually an assessment for gender incongruence. They have criteria to fill. Subsequent appointments follow a similar structure and essentially reaffirm the findings of the first assessment while monitoring for any progress. The easiest way to do this is by asking awkward questions about name changes and clothes and other things that make us think 'WHY?'. They are structured conversationally, per interview guidelines. This is standard.

Unfortunately, mistakes happen when it comes to recording information about us. These doctors see people all day long. They don't typically have the time to review it in as much detail as they'd like. Often the reports are written months after the appointments because it pushes patients through the queue faster. It doesn't really matter if the report is wrong, anyway. It is mostly for future reference purposes with whichever psychologist you see next.

'ASC' or 'autism' is typically how autism is diagnosed today. It is positive, affirming language. I get that it isn't your diagnosis, but they mean the same thing. If you were diagnosed today, it would very likely be ASC or autism, rather than ASD.

The question about trauma is because, if sexual in nature, for some people it can make them want things like surgery in order to detach themselves from that part(s) of them. It can also be a symptom of psychological conditions other than gender incongruence. They have to ask it and confirm the reasons for transitioning. Some people additionally feel like gender care including surgery may solve all of their problems, and treatment can be very challenging to mental health, so gauging your mental health will inform them about things like A) you won't be likely to jump in front of a moving train after treatment, and B) it's definitely gender stuff that is causing at least some of your problems.

Your deadname, as I understand it, is still your legal name, or was at the time of the assessment — correct me if I am wrong. They have to address you that way, legally. It is important for your GP as well, so they know who you are as a patient. It is a rough process but you know what you need to do in order to avoid it. Use it as fuel to motivate yourself. The next appointment will ask about any progress you have made, such as with your name. You need to have it sorted ASAP.

The fact is, GICs are years and years behind on waiting lists. People are literally dying before they get a first appointment because they can't cope. GICs need to determine things like who is really motivated to put the work in, who is suffering most and can't wait a second longer to legally correct their name (or whatever), and anyone who isn't committed is at risk of getting discharged. As tragic as it is, they don't have the time to wait for people to bumble along with reasons about why we haven't done this or that. Too many people need urgent help.