Can diabetes be passed down to your children?

Yes, well possibly. The genetics of diabetes is thought to not be an all or none genetics, but heavily influenced by environmental factors. Type 1 diabetes is thought to have very little genetic predisposition. Type 2 diabetes is more common when parents or siblings had or have developed diabetes. However, it is heavily influenced by weight, lifestyle factors, dietary factors, etc.
Sort of. Diabetes does run in families but just because you have it doesn't necessarily mean that your children will get it. The best thing you can do is to teach them to eat healthy, exercise, and be aware of any symptoms of diabetes so that they can seek care if they develop any of them.
Maybe. There is an increased risk of diabetes (dm) in children of dm patients. Type ii dm, which often occurs in overweight patients, can be 'passed on' if bad eating habits, limited exercise lead to obesity in the child.
Yes. Type one diabetes is inherited. With a child with diabetes, your other offspring have a one in 20 chance of getting diabetes. The population at large has a 1 in 300 chance. You did not specify type one or two, so I might just add there is some genetic aspect of type two, but type two is primarily a disease of poor lifestyle choice.
Yes and no. Diabetes type 1 is now known to be an autoimmune disease, and is not passed down. Diabetes type two has a strong genetic component, and the risk of children developing it is significantly increased; if they learn to eat healthy and exercise to maintain physical fitness, they should avoid becoming obese.
Genetic Tendency. Yes and No. Type 2 diabetes is mostly a lifestyle disease. Certain genes predispose you to developing it, but nothing is more important than lifestyle. Studies have shown that in many cases lifestyle may as well be genetic because children adopt the habits of their parents - including sedentary lifestyle, poor nutrition choices, poor stress management, etc.