Why you lost your footing will be critical. In any premise this action, you must be true that there was a defective condition, the owner or people in charge knew about the condition or should have known about the condition and they had an opportunity to correct the condition, and you sustained injury as a result of the negligent failure to timely address the condition. On your facts, you allege no defect and you therefore would not have a claim.
I would strongly encourage you to get...
You need an attorney. Even if they tender the policy limits, you may be able to make a claim on your auto policy's underinsurance provision. Yes, I understand you were on a bicycle. You auto policy cavers you in auto accidents even when you are a pedestrian or a cyclist. Without an attorney, you could jeopardize your potential underinsurance claim in addition to taking short money from the defendant.
Find an experienced Personal Injury attorney here on AVVO through the "Find a Lawyer"...
Send a copy of everything you received to your insurance company. They will assign counsel. That counsel will advise you.
If you are an Illinois resident AND the subpoena was issued by an Illinois court, AND the subpoena was accompanied by the statutory appearance fee and reasonable travel expense reimbursement, you MUST appear/respond or you can be found in contempt of court. You may be able to arrange a telephone deposition but that is up to the party that issued the Subpoena, not you.
ALWAYS get a police report. Stories change. Police reports don't. You do NOT need an attorney. Turn this in to your insurance so your car is repaired and you have a loaner in the meantime. You will have to pay your deductible but you will get it back AND you will be able to control how your car is repaired.
No. Your daughter has a claim.
The grocery store MUST have had notice of the wet spot AND a chance to clean it up or they are NOT responsible.
If it turns out to be nothing more than a sprain, you may wish to settle it on your own. Whatever you do, do NOT allow anyone to provide treatment to your daughter by holding the bill or liening the file unless you have no insurance and no money. If you do this, the bills will be more than the case is worth.
If there is an orthopedic injury,...
Hire an experienced personal injury attorney BEFORE you say anything other than you will have your attorney provide any information they may need. Just using the wrong word can cause an adjuster to wrongly deny a claim. Discussing the facts with an attorney, first, can easily prevent this. All of this work is performed on a contingency basis so there are no up-front costs.