Ah teenage boys.... (sigh!) I think it's especially hard when they've need us to organise them in the past and we've kind of kept on.... My first thought is, ask fewer questions. Go and see if his bedroom is tidy and if it isn't then tell him to do it. Or go for the "his bedroom his business" approach, which does not work in my household because we get mice and because DS (15 yo, Asperger's diagnosis) blows a fuse when he can't find things..... Also, our DS's are old enough to take more responsibilty for their own actions, and old enough to decide whether they want help on our terms or would rather muddle along on their own.
So you could ask him if he wants to be reminded about specific things he struggles with like the schoolbag and make a deal - "I will remind you to pack your schoolbag so long as you go and do it straight away. Otherwise I will stop reminding you". I made a deal with my DS - "I will remind you if you don't snarl at me"!! Even if your DS has ADHD he needs to learn strategies for managing things by himself, so if he doesn't want to be reminded then let him forget and take the consequences a few times, then maybe talk about techniques to make things easier - visual lists, packing it the night before, whatever.
Also watch your communication - the weary sarcasm thing can be quite destructive. Positive instructions are better - "please bring home all the change and a receipt". Ask him for the change and receipt afterwards, or call the station and find out how much it should cost.
Leaving the CV til bedtime sounds like anxiety. For this one, you could either insist that he does it at a time that suits you and stops avoiding it, or else let him not do it and take the consequences. In our house that would be "I will help you now, get off the computer and we will do it, I do not have time to do it later". And if he doesn't, that would be his decision.
In theory i'm in favour of letting your DS sort out the Duke of Edinburgh stuff himself too. They would eventually have found out from the instrucotr's repoert that your DS was skipping Taekwondo and he wouldn't have got the DofE. But in reality, I do intervene with my DS's DofE, nag him to do music practice etc (subject to the no-snarling rule :-)) . My other rule is that if I pay for lessons then if DS skips too many then I will stop paying for them, end of, and I do check with the instructors.
I'd be relatively easy on losing things, since he has ADHD and I was a forgetter myself. I just wouldn't give him any expensive kit (like fancy phones!) to lose.
But I would do whatever is necessary to stop him taking money from your credit cards - at least report the cards lost and get new ones, put passwords on online accounts etc. That is deliberate stealing and I would come down hard on it myself. Sure, when my DS was 8 yars old he took some cash and I treated it lightly as "unauthorised borrowing" but I also warned him not to do it again and that it could be seen as stealing. At 16, I definitely call it stealing (though I'd be careful to say "that was stealing" rather than "you are a thief" if you see what I mean!), and I'd put some heavy consequences on beyond just repayment. Given that you have let him get away with before you need to warn him exactly what the consequences will be if he does it again. And then stick to them.
Sorry that was a bit of an essay. My DS rarely fibs but if you have any ideas on how to get him to need less nagging...
Good luck!