Help me to understand something about diabetes

I'm not sure what you mean. Dehydration doesn't raise BP, it lowers it with regard to the loss of volume.

As far as blood sugar, it elevates during prolonged periods of stress as a result of cortisol. Given its anti-inflammatory properties, this is why people are at higher risk for infections and other complications when combined with periods of trauma or stress.

Vomiting and diarrhea will cause you more issues with acid base balances than with blood sugar, at least initially. If someone is not eating, though, that can definitely cause a lowered blood sugar. There's no reason that I know of that any of those particular processes will raise the blood glucose level.

Remember that food is not the only source of blood glucose; the liver can elevate BG via gluconeogenesis. As the previous poster stated, this can be stimulated by cortisol.

Metformin inhibits gluconeogenesis and a patient with nausea or vomiting may not be able to take it or keep it down.

Cortisol also inhibits insulin from entering the cell (insulin resistance) also contributing to an elevated blood glucose.

Diabetic patients with nausea and vomiting are at high risk for dehydration and ketosis because cells cannot utilize glucose because of a lack or resistance to insulin.

This calls for vigilant blood glucose monitoring, encouraging non-sugar fluids, and seeking medical care for uncontrolled hyperglycemia or an inability to keep fluids down.