OK, let me have first crack at this. I'm sure others will come, and you can find what the consensus is
1) Those figures look quite reasonable: I believe fasting should be under 6.1, so it might be worth looking into why it goes up overnight. Is it the 'dawn phenomenon'? Do you eat late? Worth working on, but probably not something to worry about per se.
2) I cut out starch rather than counted carbs, but I think the answer to 'how low?' might be 'as low as possible'. I try to stick to: no bread, no pasta, in fact nothing made of grains, no legumes, pulses, beans etc, nothing that grows underground. It did work for me, and I never missed those things. I get some carbs from vegetables and tree-nuts I suppose, but it doesn't do much to my blood readings.
3) I had hyperlipidemia and truly awful triglyceride readings when I was diagnosed with type 2, so I didn't go 'high fat' per se. I tried to get just enough fat from sunflower seeds, olive oil, sardines and salmon. I lost a lot of weight and the doctor recommended I eat more, so I started having quite a lot of boiled eggs and experimenting with high fat. I can say that KFC barely raises my blood, whereas rice is pretty bad, so those who advocate HIGH fat may have a point. For me, I try to be moderate: a good piece of steamed fish fills me up as well or better than, say, fried chicken, and I think it's better for health in general.
4) I've had some big 'one-off' meals that haven't hurt me much. I've also had one or two meals that put me up way higher than I thought. I suppose one thought is that you can eat like a king as long as you stay off the carbs: over Chinese New Year I ate a lot of lobster, shrimp, roast goose, pigeon- the works, and my blood readings were fine- I wasn't touching the rice.
...Um, another trick that works for me, but I'm still not sure is to be recommended, is to drink spirits or dry red when you have a 'cheat' meal. I've had stunningly low readings after big meals using that trick. The trouble is that you end up cheating and drinking gallons of gin to compensate. Still, it's another thing where judicious application may be worth looking into.
5) Yes: I dieted really hard when I was first diagnosed- I had neuropathy, hyperlipidemia and the doctor said I had the worst cholesterol readings he had ever seen, even including research literature- my fasting blood readings tended to be in the mid threes back then, and I was really sluggish going to work. Almonds, pistachio nuts, sunflower seeds during the day got me back on my feet. That, and black/ green tea. Something else is that you might like to experiment with having breakfast. I have two boiled eggs and black coffee, and that keeps me pretty boisterous until lunch time.
6) Try to check the label on the teas. If they do have a lot of fructose, you might be better doing without. Having said that, I've seen a lot of fruit teas that don't have much to worry about. What's the brand?