(1)cease to You must cease to play this stupid game that (which is better than that here) hurts. (2)be fond of I am fond of this sport which makes me feel vigorous. (3)in an attempt to We are not geniuses (did you mean genuises? It doesnt seem to fit the sentence well) and there is always something that gets us down wherever we live (what does place we live have to do with it?) yet we still struggle to live (we struggle to live?!) in an attempt to get success and pursue happiness. (4)I'm off today Tomorrow will be the last day of this year, I will be off for the next two days. (5)I'll eat my hat If you achieve this goal of losing 10 kg in three months, I will eat my hat. (6)be valued for Chopsticks are valued for their conventional (this doesn't fit but not sure what you meant) meaning and what it carries for a family. It represents families happily getting together and a new start.

Phrases I learned today

Cease is a fairly formal word, maybe say instead 'You must stop playing this stupid, painful game.' Example of cease to: In the case of an extreme emergency the brakes in the truck may cease to operate.

(2)be fond of
I am fond of this sport which invigorates me. 
(3)in an attempt to
We are not geniuses and there are always things that get us down wherever we live, yet we still attempt to achieve success and pursue happiness.

Another example of in an attempt to: 

In an attempt to lose weight, Deborah ate only vegetables and fruit for a week. 

(4)I'm off today
Tomorrow will be the last day of this year, I will be off in the next two days.
(5)I'll eat my hat
If you achieve this goal and lose 10 kg in three months, I will eat my hat.
(6)be valued for
Chopstick is valued for its conventional meaning and what it carries for a family. It represents families get together happily, a new start.

I'm not sure what you mean by (6), especially 'what it carries for a family'. 

Chopstick is usually plural. 'Chopsticks are valued for their conventional meaning and what they carry for a family(???).'