Collection Agency Interest Question , Please Help

Hi Everyone!

I was hoping to ask you all for some advice. I lived in an apartment complex in Arizona about 3 years ago. I had to break my lease and was charged $2,300. The debt was turned over to IQ Data International ( a very rude collection agency) . They are currently charging me $2,900 stating that the additional $600 is for interest that they are 'legally allowed to charge'. I have disputed this with the big 3 back in October 2015 for fraud ( because I thought the argument can be made that these charges are fradulent) but apparently the company verified my debt. 

I now live in Chicago and do not know if this changes the interest they can charge me? Also I called the original creditor ( my apartment complex) and as the company managing has changed, they were unable to provide me with a copy of the lease. I also asked the collection agency for a copy of my lease which I was told they currently do not have but will request and send me. 

When I asked if there would be any terms that in the original lease, agreeing to pay interest the person at the collection agency said 'probably not but it is state law to allow it'. 

Here are my questions:

1) If I did not agree to pay interest to this company, can it still be charged if it is not in the lease?

2) Does living in Chicago change the laws that affect me now or does this not apply since the contract was signed in Arizona?

3) Can this company sue me? If so what does this actually mean?

4)  I got Lexington Law to send a debt validation to these people to which they said they will not respond as it is 'frivilous'. Is this true? Can they ignore these letters?

Thank you for your help in advance !!!