I'm no fit expert by any stretch of the imagination, but it sounds to me like core strength might be part of the equation. It looks like you're trying to get relatively low judging by the saddle to bar drop. Speaking from personal experience, being able to support more weight with your abdominal muscles will help take the pressure off of your hands. When I first started out, I had hand numbness/aches right at the base of the thumb where it hooked around the hoods or drops even though my position on the bike felt just right in terms of how stretched out I was. After I started doing situps, the issue gradually began to vanish. When I ride my road bike now, I have barely any weight on my hands unless I'm particularly tired and have been riding for a long time.
Seems to me like the neck ache may be related for one of two reasons. Either the weight you're supporting with your arms, or the fact that you're down pretty low and are craning your neck to look forwards. On this second point, I can also add a little bit of personal experience. I used to get neck aches when getting low on the bike riding with my cheap, bulky helmet. I realized that when it was on properly and I was on the bike, the front of the helmet was thick enough to obscure part of my vision. I upgraded my helmet to something a little less bulky, which allows me to have my head in a more natural position while still being able to look ahead when I'm low (by my standards) on the bike.
Just my .02, to be taken with a grain of salt.