Is dementia hereditary?

Yes and no. If there is an illness that runs in your family you should speak to your doctor about it. There are many many types of dementia. Some of them are genetically passed on while others aren't. The most common type of dementia is alzheimers disease and there are 2 forms. The early onset form is highly heritable. Alcoholic dementia is not inherited though a propensity for alcohol dependence can be.
Not necessarily. There are studies indicating heriditary as a risk factor for alziehmers.
Yes. Early onset Alzheimers is very rare but it very much genetically driven (Ps1,Ps2,APP). Late onset Alzheimers has genetic linkage (ApoE4) and several candidate genes but the effect is less potent it seems. FTD type dementia's have about 40% genetic basis and this finding will likely result in the renaming of these illnesses to link misfolded protein, genetics, and location of damage.