Do the characteristics of a compound share the characteristics of the elements that make up that compound? use water as an example in your explanation.

The answer is No.  A chemical compound does not share the characteristics
of the elements that make up that compound.

Example #1:   Water.  H₂O
Water does not burn, like Hydrogen does.
You can not breathe water, like you can breathe Oxygen.

Example #2:  Table salt.  NaCl
Salt is not a greasy corrosive metal that bursts into flame
when it gets wet, like Sodium is. 
Salt is not a poisonous bluish gas, like Chlorine is, and you
can not use salt to purify the water in your swimming pool,
like you can use Chlorine.

Example #3:  Carbon Dioxide   CO₂
Carbon Dioxide is not a black solid that burns and makes dirty marks
on everything, like Carbon in the form of charcoal is.
You can not make diamonds by squeezing Carbon Dioxide at high temperature,
like you can with Carbon.
You cannot breathe Carbon Dioxide, like you can breathe Oxygen.