Some of these are strange sentences, often with strange word choices.

I'm just going to correct the grammar. That's all.

Best wishes, Clive

My business had to correspond to my competitor's business in order to make the market fair.
The balloon was infused with CO2.
I saw a cleft in the middle of thick cloud.
There are nuances between my Yankees hat and my Mets hat.
I was floundering to fight off ladies on the beach.
Bush's obscene decisions have cost many lives.
My dog's filth on its fur will be cleaned once I give it a shower.
The moon revolves around the earth.
A succulent lollipop made me feel good.
I was obliged to take out the garbage every morning.
I was disdaining a thief on TV for stealing a car from my house.
My woe from the war will never be forgotten.
A lesion on my spine healed fairly quickly.
When I feel adventurous, I have a tendency to pull off an escapade like jumping off the bridge.
I was depicting a runaway convict to a police officer.
I missed the last flight out from Mars due to my precarious decision.
I pledged myself to a clean world and started to recycle.
Every time I make a mess in my library I put back all my books on a shelf in their respective order.
I happen to be a legal guardian of my pet.

I was actually using newly learned words so I wasn't used to using it properly. The sentences make sense though right? Do you consider that it makes sense to say

 I missed the last flight out from Mars due to my precarious decision ?

There are no flights from Mars. However, it's correct grammar.

Why do you say the decision was 'precarious'?

I pledge myself to a clean world and started to recycle.

Why are you using two different tenses here?

How come I can't use predicate instead of pledge? I thought predicate means "to assert, to declare"

Yes, but 'pledge' means 'commit/dedicate', and that's what you mean here.

The word 'predicate' is usually used with the meaning 'base something on something'.

eg My decision to take my umbrella was prediacted on the fact that it was  going to rain.

eg My decision to recycle was predicated on my desire to prevent global warming.

I am liable for my pet.   

I am (legally responsible) for my pet.    

Did I use liable in correct way?

The word 'legal' is much more common here. The word 'liable' tends to be used in negative contexts, and zi don't see a negative context in your sentence.

Here's a typical context.

eg My pet bit a child, and the parents are suing me becuase they say that I am liable for her injuries.

Best wishes, Clive