My friend and I have been friends for 6 months.

It's my first time having a friend with anxiety and is currently taking a medicine for it. 

At the moment, I'm finding it hard to deal with him. Whenever I ask a question or anything like that, he usually answers promptly. When it's the question he doesn't want to answer, he just leaves it unreplied and carries on as if I never asked that question in the first place. 

It has caused quite a few issues for me. For example, I had a leaving party for our friend. I asked him to cook for us as he's a neighbour for our friend. He didn't want to, so he left my question hanging and didn't give me enough time to plan an alternative as I was waiting on him to reply.

Or, if we have a conversation and one of the topics hits his sore spot, he avoids it. He doesn't let me know, so I end up making a mistake of mentioning and he then gets upset later. 

Are there strategies I can use that will make it easier for us to communicate?