Your landlord is just trying to protect himself - if you can meet the payments there should be no issues.

Am I legally obligated by Illinois law to pay the unpaid rent and utility bill with no lease and after he broke the oral? Ilcs?

Looks like he should have let you put the utilities in your name because now he is out of luck!

What can I do since I can't really afford to keep up paying the entire rent.

You can definitely try to sue your ex-roommate. Do a google search and see if there are any free legal assistance clinics in your area.

If no contract is signed, can I leave a renting agreement before the lease is over?

Attorney Donald has given excellent advice - you can contact the landlord and provide it to her.

If you cannot an afford attorney, run a google search for pro bono attorneys or legal clinics in your area.

What are my rental rights ? and what can I do?

Normally your rights and responsibilities are spelled out in your lease.

Can i do anything in the courtroom, such as sue him for making us live with no ac/heater & for my pets health issues?

If you cannot an afford attorney, run a google search for pro bono attorneys or legal clinics in your area.

Am I responsible to pay the cost for repairs?

What does your lease say about these issues?

Why should I pay rent if the landlord doesn't what to fix the place ? Don't I have rights as a tenant with a child wit asma?

If you cannot an afford attorney, run a google search for pro bono attorneys or legal clinics in your area.

Did the owner have right to keep these things without contacting me? Or is my son responsible?

This all sounds very fishy. What exactly was missing?