If you are looking for the actual criminal case against the inmate, you will have to contact someone at the Clerk of the Court in the county where they caught their charge

He would have to have a lawyer file the motion with the Clerk of the Court. It would be difficult (but not impossible if he is sharp) to write a motion and mail it to family court. If he does this, you as the opposing party will be notified by mail of the motion and the allotted time to respond. The whole process could take months to accomplish. The judge might be reticent to rule on it until your husband can

We are not familiar with a legal filing costing $1, maybe it's true but it doesn't seem like you would get much help for one dollar. My advice would be to investigate the process in your county. You might be able to do this pro se (represent yourself), Google the information and write up the motion yourself. That would cost less than one dollar (although there is probably a fee to file with the county).

every day various elements are updated.

County jails have an area for recreation. Some have a walled area with a fence or grid over the top. Inmates can play basketball, exercise or just get fresh air. When the "outdoor air" is not an option, the jail will have a gym for the inmates to go to 2-3 times per week to blow off some steam.

Go to the County Clerk and ask for all documents related to that person's case. You will need to know where the charges were filed to get the correct information.

Usually, there is an Admissions and Orientation period. It should be completed within the first week to ten days and then he will be able to call, have visitation and get commissary

the inmate will let you know

Not likely, the only time furloughs are considered is when someone is on their "death bed" or for a funeral.

Sometimes both. Usually, the inmate is giving a receipt with the amount and a last name.