There are some spelling and grammar errors: "World No-Smoking Day" was funded by *member* states ("member" is an adjective and doesn't go into the plural) of *the* WHO in 1987 so that people all around the world could focus on the -tobacco epidemic- and fight against the disease and death it *causes*." "tobacco epidemic" is a weird phrase as epidemics, generally, apply to diseases. For example you could have an AIDS epidemic, a tuberculosis epidemic.

like julie said, grammatically very correct but yes, member countries will suit it better. "World No-smoking Day" was funded by members countries* of WHO in 1987,so that people all around the world could focus on the tobacoo epidemic and guard themselves* against the disease and death it caused."==this is my version of the statement. :)

Yes, your sentence is grammatically correct. However, I would just add that "member states" suggests one global world in which we have only states rather than countries. I suggest that "disease" should be "diseases" since tobacco causes so many problems, and change "caused" to present tense "causes" since it is an on-going problem.