Your opening question asks “Why do I find it hard to communicate properly?” Your Disclaimer provides your own answer. If you are looking for a cause for your difficulty communicating properly, combined with consuming alcohol, you have likely found it.
Social communication requires skill development. Alcohol, while in many cases decreasing inhibitions around social phobia, also impairs the ability to interact in a meaningful way.
Give yourself credit where it is due. You have taken a big step by engaging a girl in conversation and then questioning ‘how can I do this better?’
You provide that you have Asperger’s and ADHD. I’ve known many people with this combination but don’t consider myself an expert. I’m assuming that you are knowledgeable on both. Perhaps researching the subject of interpersonal & communication skills development, from the perspective of your diagnosis might be helpful in developing a personal plan to move forward.
One of the challenges facing those with Asperger’s is that they are not aware of many of the social clues and nuances that we use in every day communication. Having a mentor to work with you may be of benefit.
Thanks for your question!