Yes you know what has been preached about fats - but it is a belief, not fact, and the more it is tested, the more it proves to be false. There are a few unfortunate people who have high levels of cholesterol due to their genetics, but for most, fat is fine.
Personally my cholesterol fell on going back to LCHF eating, with trigs of 2 at 80 days and 1.5 at 6 months.
Diabetes is mostly about carbohydrate - the net, without the fibre amount that a food contains is proportional to the impace on your blood glucose.
If you reduce your intake of the high starch and high sugar foods your blood glucose should fall - but you need to test BG levels after various meals to see just how various foods affect you, and reduce or eliminate the foods which cause spikes.
I found that once I got to see 8 mmol/l 2 hours after eating the levels went on down without changing anything else - presumably as my metabolism got back into balance.