Type one is not caused by beta cell 'burn out'
I know of one case where a child was born with congenital
hyperinsulinism (a rare disease) but she wasn't diabetic then, it took a removal of her pancreas early in life to make her become diabetic (and she's actually not really T1 though she has to inject insulin).
No-one really knows what causes the autoimmune attack in susceptible people but the genes associated are mainly in the HLA system ie the system that controls your immune function .
The biggest part of your risk for getting type one was in this set of genes which control; not your insulin, but the way your body reacts to an 'intruder' It isn't heredity in the sense that everyone with these risk genes gets T1 (far from it; I believe myself to be very unlucky since I only have 1 copy of each of the susceptible HLA alleles and one non risk copy .)
Have a look at
http://dtc.ucsf.edu/types-of-diabetes/type1/understanding-type-1-diabetes/autoimmunity/
One theory that makes a lot of sense (but probably isn't true in all cases) is that some viruses are very similar in structure to beta cells. You start killing off the virus and beta cells get killed off as peripheral damage. It might not destroy all your insulin producing cells in one with one 'attack' but several over time may cause a gradual loss (hence LADA))
Your insulin production is reduced; not increased.
If you have reduced insulin rather than too much then that could make you feel faint, hungry, a reaction to not having enough 'energy' getting into your cells
Eating sugary cereals for breakfast for anyone isn't good and will most probably result in a need to snack later, especially if you are a young active child . I don't think anyone except the cereal manufacturers disagree with that.