1) Do you say "a packet or a box of washing powder"?

Question

2) Is it possible to use the word "washing-up liquid"?

3) They don't smoke or cut down on cigarettes because they know they harm our health (??) They are harmful

Answer 1

I'll give you American English terms. I'm not sure of British English terms for these things.

1. ... a box of detergent.

2. ... dish-washing soap
or
... dish-washing liquid

3. The antecedents for the different uses of "they" need to be clarified.
http://grammar.ccc.commnet.edu/grammar/pronouns.htm
People don't smoke or cut down on cigarettes because they know that cigarettes harm their health. Cigarettes are harmful.