In Florida the county health dept does well water testing for free, so you may want to check on that before paying. Call them and see what sort of sample the want and since you are not in FL see if they do this. If not ask them to recommend a lab. Do not use Calgon or some other such testers. The big thing they will check besides basic chemistry is for coliform bacteria which will reveal if your well is too near a sewage source.
I was an environmental chemist for 32 years and I have no idea why you would ask them about plumbing issues, aka expansion tank size. That's a question for the well driller to answer. Or just look on
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