Please let me know who issue an arrest warrant in Lake county ? Does State Attorney authorise it?

Arrest warrants are issued by the court. Lake County has a website you can search for active warrants.

Can an employer hold a first paycheck for any reason in illinois?

I agree with Attorney Cameron that you can check with the Department of Labor.

I want to take my money out of my "rollover IRA", because it's losing money, and I also need money right now

You will be taxed for withdrawing it. Normally there is a 10% penalty as well, but there are exceptions you may be able to avail yourself of. ...

Can I sue the hospital for breach of confidentiality.

You don't offer much detail.   Was it given to your employer pursuant to a subpoena? You should talk in person with an attorney.

The EIN number for my family's church (with 501C3) expired.

EINs don't expire.   If you need one,  you can apply online on the IRS' website. 

Would emails to my union officials using my work email be subject to foia?

There may be any number of exemptions it could apply, but nothing is guaranteed. You can't control what they deem exempt. I’d stick with the...

In Illinois, we have elected State’s Attorneys for each county. They are elected every four years.

Can not get my last paycheck

I agree with Attorney Friedman, and would also suggest talking to the Department of Labor.

I would suggest using the Find a Lawyer tab to search for a consumer protection lawyer.

Is a hospital allowed to keep my new born baby in the hospital against my wishes?

It sounds like more is going on here then you let on. You need a good family law attorney to help you deal with DCFS.