Timing: This will primarily depend on your level of fitness and to a lesser extent your pack weight, acclimatization, and the weather. But I have always been an advocate of early bird starts, say 5-6 AM to give myself plenty of time.
If you want to calculate your time and avoid an unnecessarily early start, your fitness is the biggest indicator of when to leave. Trail Camp is (only) 6 miles in, but 3,700 feet of elevation gain is nothing to scoff at. I'd first ask how long would it take you to climb 6 miles and 3,700K then add time for carrying an overnight pack and slowing due to altitude. I've personally found that I can add 25% more time to my day-hike time when I am carrying an overnight load. This time covers additional breaks and my slower pace. I would probably double that if I was not acclimatized. However, your experience will likely be different than mine, but the smart bet is to leave as early as possible.
If the weather looks like rain (but not dangerous), you may even want to leave even earlier in order to get to camp, get your camp prepped, and get inside before typical Sierra afternoon showers begin. If the weather is hot you will also want to get an earlier start.
I know some folks like to grab Portal store breakfast or drive in from LA and those mid-morning starts aren't too terrible for a lot of folks so long as you are giving yourself ample time based on fitness/weather/acclimatization. The kind of hiker you want to avoid being is the one leaving the Portal after 2 PM and stumble into TC after dark. In the best-case scenario, these folks are just ill-prepared, but in the worst-case scenario, they are putting themselves in risky situations.
Unless you are a fit hiker with relevant hiking experience and a dialed-in understanding of your pace/performance at altitude, you'll want to get started sometime between 5 AM-10 AM to set yourself up for success getting to TC.
Summit Day: It is very common for folks to get an Alpine Start (start hiking by headlamp around 3:00 AM) on summit day! If you choose to do an Alpine Start but are unfamiliar with the trail, I'd highly recommend scoping out the trail through TC to the base of the 97-102 Switchbacks in the daylight after you set up your camp. This will help you get on track in the dark.
Alpine Starts are great because you get to see the sunrise while you are high-up on the mountain. They also get you back to TC early enough to pack up and hike out the same day as your summit day. Note: when timing your descents, a general rule of thumb is that descents take 70% of the time it took you to ascend the same route.
If you are doing two nights in TC and have an entire day to summit, feel free to do a later start... though I'd still recommend a 4-6 AM start. Summer thunderstorms can pop up out of nowhere and the summit ridge is the last place you'd want to be in the early afternoon.
Diamox: I have never used it, but I believe Steve C. is a regular user. I've heard it can dehydrate you if you aren't diligent about staying hydrated, but so long as you drink well, and consult your regular physician first it has been known to be a useful resource.
I hope that this is helpful! Good luck!