Newlyweds looking for advice

I'm new to this forum - this is my first post. I do not have ADHD, but my husband was diagnosed with ADD around the age of 12. We were married last summer. We have been friends and have known each other since high school (dated for the past few years, more recently). I've known about his ADD diagnosis all along, but knew very little about how it affects adults, and I had no idea it was affecting our relationship until very recently.
When I was feeling loving and patient, I would repeatedly have to ask for his help around the house. When I was feeling less patient, I would accuse him of not caring, being lazy, or expecting me to do everything. I've been doing research online and reading about adult ADD, and now I see that we are stuck in the 'chore war.' My understanding is limited, and I do my best not to blame him, find fault with him, etc., but we both work full time and lead very busy lives – I don't have the energy or the desire to complete all [very necessary, but not obvious to everyone] household tasks. I feel like I'm walking a very fine line, constantly bothering him to help me keep up with housework – how many times can I ask before he begins (if he hasn't already) to resent me?
Another serious issue is his personal hygiene. He will often go days without showering or brushing his teeth. He gets very dirty at work, and as you can imagine, this impacts us in a number of ways. I'm often embarrassed… for both of us. And it is already having a negative impact on our intimacy, very, very early in our relationship.
He is quite bad with managing money, but again, that is not something I want to take over completely. I would prefer he learn how to help me manage it. He will ask me not to buy groceries for a few days while waiting for a paycheck, but doesn't stop swiping his card for $5, $10 at a time at fast food and convenience stores. He has little concept of how the small charges add up.
The most benign issue is how he hyper-focuses on computer games. It is worst when he is [I think] slightly depressed, worried about money, work, etc. He can easily spend 5+ hours in front of the computer, and not realize it is 4am or he missed an entire beautiful Saturday afternoon. At first I felt like he didn't want to spend time with me, but I've come to the conclusion this isn't really about me at all – he doesn't even realize he's doing it most of the time.
I'm looking for advice in a number of areas: Help for me to understand him better, and the healthiest ways for me to act; Does it sound like his ADD is not managed to the point he should see a professional for help? Are there systems that worked for you that we could try (ex. chore schedule)? Any help, advice or suggestions would be greatly appreciated. I am thankful to be tackling this early in our relationship – maybe we can avoid doing years of damage by paying attention to the issues now.
Thanks in advance.