Hi Lucy,
I'm sorry to hear you're so worried about your dad. My dad has been ill recently (nothing to do with diabetes) so I can relate. Remember when it was them worrying about us and not the other way around?!
Anyway, to answer a few of your questions... As you know, type 1 diabetes is controlled by balancing insulin with carbs. The insulin brings your sugars down, the carbs bring them up. The less carbs you have, the less insulin you will require. It also, for me at least, makes my diabetes easier to manage and helps to stabilise my sugars. People carb count so that they know how much insuling to give - you'll hear a lot of people talking about ratios. This is the number of units of insulin you need per 10g of carbs. It differs from person to person. Your dad's doctor/diabetic specialist will be able to offer some advice on where to start.
Diet/wise - in theory, he can eat whatever he wants as long as he takes the correct dosage of insulin to compensate. I try and follow a low carb (within reason - need some carbs to stop hypos) and low GI diet. Foods with low GI release sugar slowly so are good for maintaining a stable sugar level. It's also important to keep an eye on blood pressure and cholesterol and avoid foods that will raise these. You're at much higher risk of complications if you have high BP or cholesterol.
Exercise is important regardless of whether you're diabetic or not. It will help your dad to keep his sugars, bp etc under control. Try and find an exercise he enjoys - even if it is just walking the dog. It all counts!
I've always stuck to injections rather than the pump, for personal reasons. My understanding is that you need to have reasonably good control to qualify for one. I'd suggest you/your dad talks to your diabetic specialist about this.
In terms of hba1c - this is a measure of average blood sugar levels over a 12 week period. It should be between 5 and 7, usually. An hba1c of 6.5 does not suggest that your average sugar level is 6.5 - I think it's an average of around 8. There's a great hba1c converter on this website that you'll find useful. The lower the hba1c the better. High readings increase the risk of complications. They recently changed the units used to measure Hba1c, so you'll hear some people talking about readings of 50, for example. This is roughly 6.5 using old units. Again, loads of info on this site about that.
My sugars are under control now but haven't always been. I went through a period of not caring, not testing, not injecting. It can be hard to snap out of but the results are so worth it. Talk to your dad and let him know how worried you are. Suggest going along to his next appointment so you can gain a better understanding of what he is going through?
Hope this has helped and I hope you're dad's control improves. Any other questions, just ask
Take care
Em