Court Order, Insurance and Lawyer Questions

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If our court order says Ex will pay $800 for LO's insurance which represents $67 per month in child support payments, does that automatically continue for the next year? Or does that only represent the year and then drops off the child support payment total? I did not see this spelled out in the court order....

We were told at mediation that he pays for the insurance coverage. If he was ordered to reimburse for last year's insurance, what about this year's insurance?

I had LO insured under my school's insurance but now she is registered for CHIP (which will pick up as soon as our private insurance ends in August). Can my Ex dispute this and force me to insure LO under his company? Financially I am better able to handle costs from CHIP than another private insurance.

If I am forced to insure LO under my Ex, how do I go about talking to her insurance company since I would not be named on the plan? I swear I am always calling about this or that and talk to our insurance company 2-3 a month for LO. 

If I'm moving, how do I get our court order transferred to our new location (same state but different city/county) ? 

Who pays court costs when we go back to court?

If we go back to court and if he gets overnight visitations what does the court stipulate that he HAS to provide for LO? Bed? If she happens to be at his parents house then she sleeps on a palate of blankets. Booster for the table? They don't have anything smaller/shorter than a dining table so if no booster she'll be eating on the floor. Toilet seat reducer ring? And she is potty training so he will have to deal with that. Clothes? Toys/entertainment?

About how much does a lawyer cost for dealing with child support/visitation and court dates? Ex is royally pissing me off by being late on pick-ups (pick up at 8 but didn't show until 2:30 but had a call at 9:30 to say he was on his way-3 hour drive...) and late on drop-offs (45 minutes late and counting right now....), as well as not paying his half of medical bills. I've had enough and if he wants to take me back to court to argue because he feels like he didn't get a good deal then fine with me but I'm bringing a lawyer this time. 

If I get a lawyer, what all can I expect from him? What kind of information or documents do I need to have ready? Any other advice about lawyers?

TIA 

ETA: I'm in Texas by the way, if that makes any difference...