Legal Question in Landlord & Tenant Law in Illinois

In a way this is too complicated for this kind of forum. Having said that:

1. Normally no, a landlord must give applicable notice (non-payment of rent, failure to comply with a lease obligation, 30-day notice on a month-to-month situation, etc.), wait the applicable notice period, and file for eviction. You should meet with an attorney, explain everything and show the attorney any lease and any other communications and/or notices you received from or gave to the landlord.

2. Illinois law allows tenants to give landlords 14-days' notice to repair which, if the landlord does not take care of, allows the tenant to have the repair made and deduct the cost (not to exceed $500 or 1/2 of the month's rent, whichever is less) from rent. Illinois law also allows tenants in extreme situations to move out under what's called "constructive eviction" but this can be tricky and without proper notice, etc., can result in huge problems. I would review the situation you have with an attorney and at the very least have the attorney help you with proper notice depending on what you want to do. Just remember that moving out after having a bedbug problem means you are taking the bugs with you.....and if you move your furniture to a new place with that kind of a problem you could wind up being liable to your new landlord!