In these matters you gather the necessary information through the discovery process. This can be done through formal written discovery (Interrogatories and Requests for Production) or by subpoena or deposition.
You can ask counsel any question you want but they probably will not provide the answer you are seeking. Although counsel is required to communicate with you, many will keep anything lengthy or important in writing. A phone call or two does not replace the use of the formal discovery process.
If you are not able to locate an attorney to take on your matter, you should at least get a consultation. You need guidance on how to proceed, what discovery is available, what should be pursued, what issues may come up, etc. Depending on the facts and circumstances this could get very ugly.
To retain counsel, if you have funds up front, then use that and put the balance on a CC if available or ask a family member. The CC and/or family should provide a monthly payment plan.
Please act immediately to at least seek a consultation.
You can ask the attorney anything you choose -- he or she has an obligation to communicate with you regarding the case. There are, however, limits on what the opposing attorney will share. He will not, for example, share the communications he has had with the mother of your child, as they are privileged. You can, negotiate, etc., with him, but he does not represent you and is not representing your interests.
Keep hunting for counsel to even the playing field!
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.
As mentioned above, you can ask any questions you like but the attorney will not know the case or evidence until hired and discovery is conducted. You will want to know that the attorney is a family law attorney and that at least 75% of the case load is a family law nature. You can ask about the opposing counsel, though with the number of attorneys in Cleveland, we all don't know each other. You also want to make sure you connect with the attorney, meaning you are comfortable talking with him / her since your input is necessary to managing the case.
When you meet with the attorney, take all the current court documents with you so the attorney can review the documents while you fill out the office intake forms.
This answer is being provided as general advice only and is not to be relied upon for specific circumstances. By answering the question, no attorney-client relationship is created. As for any matter, it is best to seek consultation in person with an attorney who practices in the area of law in which you are inquiring.